{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Cookbook of Neural ODEs\n",
    "\n",
    "Torchdyn implements out-of-the-box a variety of continuous-depth models. In this introductory tutorial, we show how we can switch between model variants with minor effort. We will touch upon the following Neural ODE variants:\n",
    "\n",
    "* **Vanilla** (depth-invariant) (same as the [torchdyn quickstart](./00_quickstart.html) tutorial)\n",
    "* **Vanilla** (depth-variant)\n",
    "* **Galerkin**\n",
    "* **Data-controlled**\n",
    "* **Stacked (piece-wise constant weights)**\n",
    "* **Stacked with discrete state transitions**\n",
    "--------------------------------------\n",
    "\n",
    "For more advanced models check out \n",
    "\n",
    "* [Hamiltonian Neural Networks](./06a_hamiltonian_nn.html)\n",
    "* [Lagrangian Neural Networks](./06b_lagrangian_nn.html)\n",
    "* [Continuous Normalizing Flow](./07_continuous_normalizing_flow.html)\n",
    "* [Graph Neural ODEs](./08_graph_neural_de.html)\n",
    "* **ODE-RNN and hybrid variants** (WIP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys ; sys.path.append('../')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torchdyn.models import *; from torchdyn.datasets import *\n",
    "from torchdyn import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Data:** we use again the moons dataset (with some added noise) simply because all the models will be effective to solve this easy binary classification problem.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "d = ToyDataset()\n",
    "X, yn = d.generate(n_samples=512, dataset_type='moons', noise=.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "colors = ['orange', 'blue'] \n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "for i in range(len(X)):\n",
    "    ax.scatter(X[i,0], X[i,1], s=1, color=colors[yn[i].int()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.utils.data as data\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "X_train = torch.Tensor(X).to(device)\n",
    "y_train = torch.LongTensor(yn.long()).to(device)\n",
    "train = data.TensorDataset(X_train, y_train)\n",
    "trainloader = data.DataLoader(train, batch_size=len(X), shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Learner**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn as nn\n",
    "import pytorch_lightning as pl\n",
    "\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model = model\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model(x)\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x, y = batch      \n",
    "        y_hat = self.model(x)   \n",
    "        loss = nn.CrossEntropyLoss()(y_hat, y)\n",
    "        logs = {'train_loss': loss}\n",
    "        return {'loss': loss, 'log': logs}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.005)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** In this notebook we will consider the depth domain $[0,1]$, i.e. $s\\in[0,1]$. Note that, for most architectures in *static* settings (aka we do not deal with dynamic data) any other depth domain does not actually affect the expressiveness of Neural ODEs, since it can be seen as a rescaled/shifted version of $[0,1]$. Please note that, however, other choices of the depth domain can indeed affect the training phase\n",
    "\n",
    "The depth domain can be accessed and modified through the `s_span` setting of `NeuralDE` instances."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vanilla Neural ODE (Depth-Invariant)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\dot{z}(s) &= f(z(s), \\theta)\\\\\n",
    "        z(0) &= x\\\\\n",
    "        \\hat y & = z(1)\n",
    "    \\end{aligned}\n",
    "    \\right. \\quad s\\in[0,1]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model is the same used in [torchdyn quickstart](./00_quickstart.html) tutorial. The vector field is parametrized by a neural network $f$ with *static* parameters $\\theta$ and taking as input only the state $h(s)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# vector field parametrized by a NN\n",
    "f = nn.Sequential(\n",
    "        nn.Linear(2, 64),\n",
    "        nn.Tanh(), \n",
    "        nn.Linear(64, 2))\n",
    "\n",
    "# Neural ODE\n",
    "model = NeuralDE(f, sensitivity='adjoint', solver='dopri5').to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 322   \n",
      "/home/jyp/michael_dev/testenv/lib/python3.7/site-packages/pytorch_lightning/utilities/distributed.py:25: UserWarning: The dataloader, train dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 20 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f5de13a20f024fd8b6c63bb617518619",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jyp/michael_dev/testenv/lib/python3.7/site-packages/pytorch_lightning/utilities/distributed.py:25: UserWarning: Detected KeyboardInterrupt, attempting graceful shutdown...\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train the Neural ODE\n",
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=200, max_epochs=250, progress_bar_refresh_rate=1)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Evaluate the data trajectories\n",
    "s_span = torch.linspace(0,1,100)\n",
    "trajectory = model.trajectory(X_train, s_span).detach().cpu()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vanilla Neural ODE (Depth-Variant)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\dot{z}(s) &= f(s, z(s), \\theta)\\\\\n",
    "        z(0) &= x\\\\\n",
    "        \\hat y & = z(1)\n",
    "    \\end{aligned}\n",
    "    \\right. \\quad s\\in[0,1]\n",
    "$$\n",
    "\n",
    "This model, contemplated by the seminal paper from [[Chen T. Q. et al, 2018]](https://arxiv.org/abs/1806.07366), is usually obtained by concatenating $s$ to the state $h$ as input of $f$, i.e. $f([h(s),s])$. For a simple and flexible implementation we developed a dedicated layer, `DepthCat`, which takes care of automatically concatenating $s$ to the state at each call of the `DEFunc`. The final user only needs to specify concatenation dimension to which $s$ should be appended. Specifically, for an MLP, $h\\in\\mathbb{R}^{batch\\times dims}$ and, thus we should use `DepthCat(1)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# vector field parametrized by a NN\n",
    "f = nn.Sequential(\n",
    "        DepthCat(1),\n",
    "        nn.Linear(2+1, 64),\n",
    "        nn.Tanh(),\n",
    "        DepthCat(1),\n",
    "        nn.Linear(64+1, 2))\n",
    "\n",
    "# Neural ODE\n",
    "model = NeuralDE(f, sensitivity='adjoint', solver='dopri5').to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 388   \n",
      "/home/jyp/michael_dev/testenv/lib/python3.7/site-packages/pytorch_lightning/utilities/distributed.py:25: UserWarning: The dataloader, train dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 20 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a09fb4621f724c83a7d90fa54c0637d6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train the Neural ODE\n",
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=200, max_epochs=250, progress_bar_refresh_rate=1)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Evaluate the data trajectories\n",
    "s_span = torch.linspace(0,1,100)\n",
    "trajectory = model.trajectory(X_train, s_span).detach().cpu()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Galerkin-Style Neural ODE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Galerkin-style Neural ODEs proposed in [Massaroli S., Poli M. et al., 2020](https://arxiv.org/abs/2002.08071) make the weights of the neural ODE to be *depth-varying*, i.e. $\\theta=\\theta(s)$ obtaining a model of type\n",
    "\n",
    "$$\n",
    "    \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\dot{z}(s) &= f(z(s), \\theta(s))\\\\\n",
    "        z(0) &= x\\\\\n",
    "        \\hat y & = z(1)\n",
    "    \\end{aligned}\n",
    "    \\right. \\quad s\\in[0,1]\n",
    "$$\n",
    "\n",
    "where the depth evolution of $\\theta(s)$ is parametrized by a trucated eigenfunction expasion, usually an orthogonal basis of some functional space, i.e.\n",
    "\n",
    "$$\n",
    "    \\forall i \\quad \\theta_i(s) = \\sum_{j=0}^{m}\\gamma_j\\odot\\psi_j(s)\n",
    "$$\n",
    "\n",
    "The model is then trained by optimizing for the eigenvalues $\\gamma_j$. Note that if $\\theta\\in \\mathbb{R}^d$ there will be $d\\times m$ final model's parameters. In this tutorial, we use a 10th-order polynomial expansion to model $\\theta(s)$.\n",
    "\n",
    "**Note:** In `torchdyn 0.1.0` only Fourier `FourierExpansion` and polynomial `PolyExpansion` bases are currently implemented out-of-the-box. Even though a wider selection of bases is planned as a future addition, e.g.  piece-wise constant functions, radial basis functions, etc., users can easily create custom `Expansions` on their own given `torchdyn`'s modular design."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# vector field parametrized by a NN with \"GalLinear\" layer\n",
    "# notice how DepthCat is still used since Galerkin layers make use of `s` (though in a different way compared to concatenation)\n",
    "f = nn.Sequential(DepthCat(1), \n",
    "                  GalLinear(2, 32, expfunc=FourierExpansion, n_harmonics=5),\n",
    "                  nn.Tanh(),\n",
    "                  DepthCat(1), \n",
    "                  GalLinear(32, 2, expfunc=FourierExpansion, n_harmonics=5))\n",
    "# neural ODE\n",
    "model = NeuralDE(f, sensitivity='adjoint', solver='dopri5').to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 1 K   \n",
      "/home/jyp/michael_dev/testenv/lib/python3.7/site-packages/pytorch_lightning/utilities/distributed.py:25: UserWarning: The dataloader, train dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 20 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "85ef207648b841b6b3b0674e280bf234",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train the Neural ODE\n",
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=150, max_epochs=200, progress_bar_refresh_rate=1)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Evaluate the data trajectories\n",
    "s_span = torch.linspace(0,1,100)\n",
    "trajectory = model.trajectory(X_train, s_span).detach().cpu()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data-Controlled Neural ODE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data-controlled neural ODEs, also introduced in [Massaroli S., Poli M. et al., 2020](https://arxiv.org/abs/2002.08071) consist in feeding to the vector field the input data $x$ (the initial condition of the ODE), leading to\n",
    "\n",
    "$$ \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\dot{z}(s) &= f(z(s), x, \\theta)\\\\\n",
    "        z(0) &= x\\\\\n",
    "        \\hat y & = z(1)\n",
    "    \\end{aligned}\n",
    "    \\right. \\quad s\\in[0,1]\n",
    "$$\n",
    "\n",
    "In this way, the Neural ODE learns a family of vector fields rather than a single one. \n",
    "\n",
    "In practice, we concatenate $x$ to $h$ and simply feed $[h, x]$ to $f$, which should indeed be defined to accomodate the extra $dim(x)$ dimensions. Data-control inputs can be defined at any point in `f` via use of `DataControl`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# vector field parametrized by a NN which takes as input [h, x]\n",
    "f = nn.Sequential(DataControl(),\n",
    "                  nn.Linear(2+2, 64),\n",
    "                  nn.Tanh(),\n",
    "                  nn.Linear(64, 2))\n",
    "\n",
    "# neural ODE\n",
    "model = NeuralDE(f, sensitivity='adjoint', solver='dopri5').to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 450   \n",
      "/home/jyp/michael_dev/testenv/lib/python3.7/site-packages/pytorch_lightning/utilities/distributed.py:25: UserWarning: The dataloader, train dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 20 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fbee0ede759643bea521d10290a78631",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=150, max_epochs=250)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Evaluate the data trajectories\n",
    "s_span = torch.linspace(0,1,100)\n",
    "trajectory = model.trajectory(X_train, s_span).detach().cpu()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stacked Neural ODE (aka Piece-wise constant parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While looking for an \"easier\" solution than Galererkin Neural ODEs without trading the expressivity of the model, **stacked neural ODEs** may come in handy. Instead of approximating the solution of an infinite-dimensional problem (e.g. Galerkin-style), we can also use piece-wise constant weight functions. Let us subdivide the depth in $N$ intervals\n",
    "    \n",
    "$$\n",
    "        \\mathcal{S} = \\prod_{i=0}^{N}[s_i,s_{i+1}], \\quad s_0 = 0, \\quad s_{N+1}=S  \\quad(\\forall i  \\quad s_i\\leq s_{i+1})\n",
    "$$\n",
    "\n",
    "We can then define the weights as piece-wise constant functions \n",
    "\n",
    "$$\n",
    "        \\forall i  \\quad s\\in[s_i,s_{i+1}]\\Rightarrow\\theta(s) = \\theta_i, \\quad\\theta_i\\in\\{\\theta_1,\\theta_2,\\theta_N\\}\n",
    "$$\n",
    "    \n",
    "The solution of the neural ODE becomes \n",
    "    \n",
    "$$\n",
    "    \\begin{aligned}\n",
    "        z(s) &= x + \\int_0^S f(z(\\tau),\\theta(\\tau))d\\tau \\\\\n",
    "        &= x + \\sum_{i=1}^{N-1}\\int_{s_i}^{s_{i+1}} f(z(\\tau),\\theta_i)d\\tau\n",
    "    \\end{aligned}\n",
    "$$\n",
    "    \n",
    "This is equivalent to stacking $N-1$ neural ODEs with **identical structure** and **disentangled weights**\n",
    "    \n",
    "$$\n",
    "        \\begin{aligned}\n",
    "         \\dot z =  f( z(s),\\theta_i) \\quad s\\in[s_i,s_{i+1}]\n",
    "        \\end{aligned}\n",
    "$$\n",
    "    \n",
    "which are **stacked sequentially** and trained with *classic* adjoint method.\n",
    "\n",
    "In principle, $f$ can be chosen arbitrarily. Hereafter we consider, e.g. the `data-controlled` case.\n",
    "\n",
    "**NOTE:** Let $\\Delta s_i = s_{i+1} - s_i$. Since the individual Neural ODEs are *depth-invariant*, we can just solve the ODEs in $[0,\\Delta s_i]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We choose to divide the domain [0,1] in num_pieces=5 intervals\n",
    "num_pieces = 5\n",
    "\n",
    "# Stacked depth-invariant Neural ODEs aka Neural ODEs with piecewise constant weights \n",
    "nde = []\n",
    "for i in range(num_pieces):\n",
    "    nde.append(NeuralDE(nn.Sequential(DataControl(),\n",
    "                                      nn.Linear(4, 4), \n",
    "                                      nn.Tanh(), \n",
    "                                      nn.Linear(4, 2)), solver='dopri5', s_span=torch.linspace(0, 1, 2))) # here we chose Δ𝑠_𝑖 = 1 ∀𝑖. (s_span)\n",
    "model = nn.Sequential(*nde).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type       | Params\n",
      "-------------------------------------\n",
      "0 | model | Sequential | 150   \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5914cb0b295840d0898283169d5fd295",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=300, max_epochs=350)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Evaluate the data trajectories\n",
    "s_span = torch.linspace(0,1,20)\n",
    "trajectory = [model[0].trajectory(X_train, s_span)]\n",
    "for i in range(1, num_pieces):\n",
    "    trajectory.append(\n",
    "        model[i].trajectory(trajectory[i-1][-1,:,:], s_span))\n",
    "                      \n",
    "trajectory = torch.cat(trajectory, 0).detach().cpu() \n",
    "tot_s_span = torch.linspace(0, 5, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(tot_s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8w803a0HbXbv2nhrk9/ddWyUQUPGMHTuw+AotX65uZ6H45s2D88+HU05Ry5dbe90ytIwU0U0EJhpjlotINfAScIkxZm1/14wE0YGK4sc/hv/9X9i0ae8xXs4K9Y7tQU/xVVVplzInvpx1i8XUiu5LfBddBJde2nMZaMvQMCImsRpjdgA73NfdIvIq0AT0K7qRQjislaGnTYO771bHR+G6d4mEZrf4/fq6sLBRKqUOmY4OFUtDg4rP61VxpVK6n9t6iy+bVW9nWxu88oo6X66/Xs+1DA8lI7pCRKQZmA8sHt6WDB5+v5brGztWZ6E/9xzs2KHHjFFR1ddrmCCXmVIovkQiL776et1yZSFyli8nvHBY79HVpV7QwnXV77hDr73ySuvhHC5KpnuZQ0TCwCLgu8aYv/RxvLAa2PGbN28ucgsPnc2b4T//U+tr9i7PXpgals3mx269qajIJ1DnxOf1qlCNya8yG4mo0yU3tchxtFDSbbfBBz6w9yq0lsFhRIzpAETEDzwMLDTG/Hhf54+UMV1fZLM6i/w739Gk6RwiKiivVzefT61YKtW3+EIh7XaOG6fiy12Xq9WSyejr7m61dImE3nPGDLj9ds0ZtcIbfAYSXckUmxURAf4LeHV/BDfS8XjgnHO0XubnP5+fupNzjCSTusViKopwWMd9vb2PuW7n+vVaLrAwgJ7zeIbDKsraWn0/m1Vr++1va2aL4xT91y9rSkZ0wKlo3cszRGSFu5033I0aasaNg5/8BB57DObMyb+fSumWyeSFFArpmK2ubm9HSCKhhZPWr4ft29UqplJq1XJdz9pavU5E75tb+uuZZ6zwiklJdS8PlJHcveyLaBR+9CPdCovb5pwlfr8mUvv9ahFTKe169hV0r6zMhxoCAd0iEfVeRqO65e45b56mrb3nPX0vAW05cEZE99KiVuiWW2DNGvjwh/NjrUwmb/mSybxDpLJSu45jxuxt+WIxtXwbNuhYLhbrOZcvFMoXSnrtNbjpJrV4dhGUoceKrgSZOhXuvVfDCmeckQ9256xaTnyxWL7qWHW1djsLx3zG6Plbt2pXcvfuvIMlHFarmbOYOeEtXGiFN9RY0ZUoPp/mTT70kIYWjj8+fyyX/pVO6xaPqzWsrNRxW21tzxicMXr+9u3Q3q6zGuJxFWpOeDmLd/PN8H//t38l5C0HhxVdiVNVpalbjz6qs9Nnzcofi0bV2jmOiib3uqpKhVdT07PbaYwej8U0cN7ermO4QuGtX6+zI/785/1L0LYcOFZ0I4Rx4+DqqzW297WvqZME1P2fK/FgjFqoXDwvNxG2d7fTvZJkMktXVxzHyZBOZzEmjuPE2bgxzrdvjnHvbzJ0tMQgk4R0FGKtkOrSfScFWQeyGX2wZb+x3ssRSCYDL74Id94JDz/c09MZCukYL5stCLB74xggHjOkUkI8ATqRo3cxlxQgBPw+DA4TGtJc+9FNXPMpw/jaPZBsh0wcamZDoA4C9dD9uv70VwJ+CI6BQDU4aRBvfkBaZoyIhGfL/uPz6fLMxx6rSzDfdRc8/7x6NRMJQyKRoKoSvJIlnRbSxAh6hdqQQzLkgWwF8VTun62HvPg0Qp9KZwBhx+4Ad9zTTGt3Kzd8vJXmhk6IbVbrVt0M2TS0LoVADdTMga71UDEVqqdDfDuE6qFqJmQ6wT8WxAGfnVtkRTeCCYc1f/KkY2M8+Kfd3H2vn+VraskaL9EYJGIOVWGDz+MlnjQ4ePD7slRVpsF4yDhZvB4hkeldyVa/FhnHob0jwG/+MIGW3cKt1+5kVqMBj4DHB6lOcGJALSRbIbkLQk2w5wWIboNxp0PiRYhsgZp5EKwFXxj8VeCtAF95zqy1ohupOA7EdsKepTTF3uAzZ+zmHU2N3P/0XH73xOGs3zoOBz9dEQj4MlRWpDGOh2QGPL4MXn+QTNaLR1LUVGaIxwOkTe+vg5ek45Ds8PPQwgkcNa2RG69Yh1pHDyTeAuNodzK+C7yV4KuCtk3gr9XuZdtyFWY2Ad4qqJgMwSo9t2o6BML5moRlghXdSMPJwM6/Q9sSEJ9anWwckQDHztnJ3GktvOO4Hdz/1GE8+PfD2NlaSSrjI9Xto9KfpCLoIMYDJo3XHyCbDZBMOVSF48QSIVJpHz3Hepqi0h338b5TXwXJuuM0A/GdavGMD9JdUDFJu58mBTWzILoZUh3gr9Z2xzdCbDvUzIBUO7SvgYbjIR2DivEQGg+e0Z8SY0U3UnAy0L4KOl+D7nWQ7lDvYcUk8IYAA5kMoVCK9574GkdN38Upx7XwwDNzWLR0Iu3dIWLpIPG0j3BFgpDfEEtAxsni8XhIJIJU+lL4vQ7RhBfoOfUg4E3S1h7CZD0IHh3PpTrUiZLao20JNsCepeAfA8YP0Y1q7fBCcg9IBnxj1SomWyCY1n8gThQazwB/DVAx7M6XaFQTwmtqYPLkwb+/9V6OBJId8NZTsOc5MAKBcUBKv8gmo192X4124zIRfc8Ijgnw8sYZPLPqSB58pIEVrzUQTWrU3EuSYMBgjA+DwXHSCD78PqPTgbI+clYOIBhwmDO5hcvPX8Fnrs5SU5WEzpVQNUsF5K8BTxAiG2DsSWoF41vAVw9OREMMobEgfki3gqcSskmIboLQZKg7DCqatHtaOQlCE8FX3DlHO3fq8mdr1mgYZv58eP/71XF1oFjv5UimbS1sfwQSLeAJQ2YPJLZBcCwE6yGxRy1HMKlWR4B0J2QzeCXLglnrmTFpD7Oa5rN4+U4efXYq6zbXk3QCxFIgZPCLIF4/mUwWJ+NDMIBDoeiSKS9r3hzHT+87lZc3dPHlj7/AgtmCZDMqnkAtdL2m7comtGvpC+k/AScKvmowWUjs0G5xqh2S28BXB2LU8xnbCeJRZ0vj6TDmiCH/eNNpWLdOpzgtXapZO5WVWsT3qKMOTnD7woqulIm3wu5FsOcl8BjwjgF/WL/IiV36RQ7WQ7odkm2QjuvYyFsDpgsyKTAO9ZW7ufiUF5jZNI9ZzVGeX1bPU0ua2LazFoOflMniyTgIXrJZ447o9h5bZfGysy3Mw89Use6NU/n4BWO4+v2rqK6thHgLZFPqvex6HchorM7pVqeJeCG2w10XrB1SreCtBglCKgqSgsg2FWqoARLtOtbzD36IwRhNAn/2WQ25rFunZTAcR2djLFighXsPO2zQHw0MguhE5EZjzO2D0RgRORf4GfoX/5Ux5vuDcd8RSbITtj4C3RvBG9QxXGozJKs1/mUEUm2QjYKnRv+S6QjE4lAxQcVputXqOGk82TRHT13FpLHTmdTQzZGHR1n092r+tryZznglWfxAFnAwOe9knwjRhLDy9UZ+cE8tL64Yzw1XruOUeSuQiiZIbodUC5gQmHaQgMbh49tVlOmYxu181eo0Sbfqe04cnCz4K/RY9E0wMRj/ThXiIWKMFmdauFBzS1ev1qXNcgWcKio0ZW7SJJ3idPTRQ+dQPWDRicgfCneBY4FDFp2IeIE7gbOBbcBSEXlooBJ8oxZj1Mp1vQKRN9SJImlNRXF2QGqXBpsDNTre88TUQ+ir0jStyBYINIKE1NvoxMCkIZOmoSLFWSc2Mb62m3HhCcw/fBd/ebyZNZunYvChYnPYO1ulVxPxsrOtigefm8eajRP40Fk1XPex7YwLrNEwQqYdvH4NiKd3aBsS3ZCNa/cxHVPL50T0WR6fxu0cA5GN4HH0PunugxZdJqOFfu+5R63a1q35dDnQqVO56VHhsAruggt0G8oSFgdj6bqMMVfndkTk3wepLScCG4wxb7r3/T1wMaOgBN8Bk4lB96vgCWnXLLVFLV82rsccA9k3tOtVMVGtmjeiX05/JTgJiG2FYDVItQaj0536fjJNwJ/iuHmN1NdEaKgZz+SGlfx96Rs8uuQ4Wrvq6atr2R/JlJ81G8fzo/veyfMrNvFP7+/kfSevxuf36/PSO3X8looCWbV6sR16zDjgDbi/Z1CP+b1ARrudlZP1+H6yYwf88Y+an7pihZYeTKX2LvAbDGpOaiCgaXKhkBZruuoqOPtsPTaUHIzo/qXX/s2D0RC0xuXWgv1twEmDdO+RhclCRSOMP1W9esk2FVH3GxDdAondOq5LdajV84U1GO2r1txHfzVgILobvF0QGgOeKsh2QyYBTgKPk2LGpLFUVSQYX19LTSjCsbMeZdFLs3l6xTwi6Wr2Ze0K6YpVsHDpPB5fOptZE7fzsfc8wafO+j+a6jZqsnQmAiTRLixAUB1DniqoqNfQR9U0qJoKYTeVLDwb/Hkr194OS5aooF5+Waci7dih47HCcoX9MXasiixXwKmqShPHjz0W3vc+OP304pSf3++QgYicAVwOdACrgVXAamPMoMy8EpHLgHNzVlRErgBOMsZ8rtd5I74E3z4xRoUnot68QrJZaFkGWx+Elud0rGQcHR95qzQR2et+qzwhPZbNqnfRE1RPohPX8ZUnCJ4gBuGt3dV0dIdob3foijfwj1VjeXTZfNZtaSbqhFHrd6CBawPEaAjtYG7jKk5oXkJjQ5K4M5FkYAoRM4EuZzId0Xq6IkG6EzV0dfmJxTzE47y9HSzhsMbacotuBgLabayuVrFdeKEKbs6cwbdug1KCT0Q2AV9Ao6ZHu9sRxphZA113AI08BbjVGPNed//rAMaY2/q7pmzidH0R3QLbn4XtD2sOpKcCcC1kqEGto69Ck5Oj29Whko5C0rWSxoCTVHc/hu0dk8AYasJxTLYC4w2SzWaJRyGWrqYqlGHR6/P5zdPns3rzTHZ2jCVFJZokfaAeBy+55OrBwudTQeXWc89VwM7VgamuVss2f35+FduTTx66sdtgxek2G2MecF//8dCbtRdLgdkiMh14C/gw8NEheM7ooKJJM/19Vep4yP0pfTXg7IJMFEybG4j2alCarHZDK5t1DJWMaGwt24FX0lQGWwj7I6go1INZF8igjpUAH1rwOh9a8D9ks5DOAKTYuLOJB5edxZKN81izZQ7bWqcSZSxQgYoxVPB68MgtohkMqsAKx2d+v3YTAwG1dE1NcMIJGgI4/nh9bzjZp+hE5DfAcuBFEfnSUNWkNMZkRORzwEL0r/5rY8yaoXjWqMDjhYYToX2tpoZFNkEmrd6+UCMEw27YoFa7nL4KnQtn0pqy5atVJ0xqB8TeorF2o3vjXDcyC+QEBzrXzgEMHk+WoGuo5k7dzISxf+TT2SyRxDhWd1/Gdu8HaPMcw7r1FWzZAhs36nisre3g57v6/flZ7rnXOUvm9aola2jQtK3mZjj1VPVG1tbqWG6onSMHwv5YunuAY9AlrM4RkRuAle62yhgzaFbPGPMI8Mhg3W/U4wvBnKs0LLDhV9C9RROKM2nIToXKgFpCJwqegBtY73KD1p3qyDC943EOEETHYwYVYM5LkXXf60ldlReaLmHMYdcyZdyJRBM+WltVII6j6/S1tqrTo71drdC2bVqrZft2PZZbay+33l6u7GBFhd5nzBh9PX68Fm5qblax5aphjxkDRxyRt26lJLLe7FN0xpingadz+yLiA+ahQjyBoelqWvYXbxBmX6Mu9vW/0GB6andeG5VuvmNyj2aveGs07pdN6Vgw3d3HTXPei94C67UvY6HxLBX+mMO1LWTfXsgkxwc+oGJKJDQYnclonZaqqp5LO3s8+WpljY358hOxmL4OhdQ5Ul2t20gtB3/AIQNjTAZ4xd0spYDXD7OuVE/n63ep8NK7IerOUwvVavA53Q6BMeANa7ZIxxrI9OX93VcfcCxMOAfmXgP1R+vzjdFxpBPtM7aWc9HvdaexB/Ubj2hs7uVoweuDmVcAXnj959D9pjpRol71iQTqVIDJDk0jywQgtu0AH1IJdSfAzE/AxHdq0F1QwXl8msiciYK/rqwmpR4oVnSjCa8PZn4UcFzhbdLgebeBWp9OvzEpSHTA7peAvrqWhQSBarWO4WaYdAE0XwwVDWh2SUZDEtk4ZLLaZU226TQefw14/PlNfFaILlZ0o423LZ4Dr98BXZs0o79LoHampollYuC8tY8b+cFbq0H10DjNakntgh1PQdUkFZ6/Rr2g/mo3jcv1dOZ+OjHIuF1V8UBwXFnMDN8XVnSjEa8PZl4JJgnrfqEJ0MkW6FpzKZcAABL3SURBVPJD9VQtCiTVYBID3MQNLSRbNPm6Yx14F+ksdX9OiFOhZqbGC0MTIFSnWS4IBMdrUrZxdJZ5ukOD8oHaIn0IpYsV3WjF64dZn4ZUBDb8GuI7dAKpxwuVTVB3JLQvBmL938NXpUWHshnNXiGtsb50VKt9eVbBrqAWF/KNgfBkqJihHtOqKRCertYwMMZNbYuoVeyd2lZmWNGNZrx+mHu9zjB483c6zy22XcdYFY1QOQdir5APgPcinVDRSUBLJwjg94BX3AzjlI7nkq1a/TnyJnhe0NqW/krNfKmeDeGZ+jyvRy1i1VS3a1pRlgK0ohvt+CvgiJu0WteWv+jPuCu88GTt9qU39XNxO8g0FYu4jhMnA45HBU3QLbXncWN/SZ14mu7WMhLR7dD2kgbl/TWaARNsgvqj1BIG69xK0WPVGvqCRfxghg8runIgWANHfFNLIOx6EjIdEHNnh9fOhtYOdPJIb9KQ2K5dQk/AtWC5MEEmL8KsW5ZPqtT5EjS63kEmBp6UTqxNtEFkKyCw+2kdE1ZOgfAcqJmmuaT1x2qy9ij3clrRlQvhCXD0t2HpHmhdDJk2iPnB2wx1R0DHYjTXsheZDJpo6Wh5CBEwXk1B81XofDgP6iwxaQ0bZEVrovgqdawX8mnqWSYKmW53Umu7BvH3LNZ5gP5qqD0G5n4Jxkwv7mdTZMqvQ13OjDkMjvoW1M0FPJBpcR0iQfDO6OeiTq3H4qnUepaeGg2EZ1PahUzu1oB7Jq3z+PxjtHy6PwQ+r475nIRax0AtVDXrmK6iSbumWQdiLdC5Djb/Dv52EWxf5DpuRidWdOXGhHfAvBugciqQ1dhbfA/UTgVPQx8XJLSQULpLA98S166mp0pL/vnCgNGxXHS31rtMt2mRIV+tWjpvlV7jOJCNaXdURHNBK6dq4L2iCRCIvg4vfgpWfRf2rBqVy3CVhOhE5Ici8pqIrBKR+0WkbrjbNGoRgamXwfTLwV+Pjtve0rqatXOBPhIknZR2Jf0VmnniRNwyem1ARruagTp1jHhDmrrpdKkAU3tUsB6/6zgZ63pEvW6uZkzrXvrDWoqdgNb13Pg7WPUd2PZYP0nZI5eSEB3wBHCkMeZo4HXg68PcntGN16ehhInv1S6hiUJsk3ob6cPaOa0qJI9fReV1QwIEVZCpbrWW2ZiK2hPWbqZ/jFq4bBKiO9Qpk2xRK+itUo+lv05nQThu9S/PGMAtSrtnOaz/JWx7FKL7yqAZOZSEI8UY83jB7ovAZcPVlrIhWAVH36pTflr+DtkuSG2j7//DKfV8htxalY5XwwgBD2T9aPcyq+MzE9VanF5R6+gNailA3BVbjQPpPe59RceToXqd+eBBy060dwHd2vXdtQhiu6FzNcz4FFRPGfGxvZIQXS8+CfzvcDeiLKhpghP+Fdb+EN56WoPcpFAvZi9PprMZolXgqXW7kCHwBdSTKR4Vo/GoiEwWMo46Wxx3bp6ggvLX6I6T0LotmShE42pFfUGt+lwzW8tI4HpEu1+FjXugfTVMOBOmf0hDCyOUoolORJ4EJvRx6GZjzIPuOTejf+37BrhPYTWwIWhpmVEzHeb/EJpfgl2LoeMl6NwAkVfZO0XMtWJZIO3OQPBVgz/o1q/0uQ4UL/gFCLqlUTIqskyniszr1y5qoFq7mcZxY34pzZqRrF6Lm3qGF5Ld0LVBz0u2wMxPah7pCKRkVu0RkU8A1wJnGmMGSAjMU9bVwIYKJw3d62HnP2D514C2/bjIR16AlSpA8bmWz6OOEoPmcJLV900aTT9zi5x4q7Q7aiRfej22HhWdX5/hrdF0snAzNLwDZl8NFaU5C7bkV+1x1zD4GvCu/RWcZYjw+qHucN0C4+HFS8gXiB0L5IrGFpIB2rWUesYLVIGnGgKVbgzQXXZLfEDarU4WdMsApt1K0HtUrL6AO84bD6kkZLbkn+HscWs77NGucKYbZl6li0yOoCyWkhAdcAfan3hC9MN70Rhz3fA2ycK082DDRdDqVl6UIASawOtomXenHe2CFvaWHKBLHTMJgCqQsJYG9Luzy70+d0VXcS1itVo+Y1wvZrduwQrIVLjPyC1wktZSE+1JDcrHt8LMz8KEkVMMvCREN1gFay2DjNcLC74Hjz0LdIDZpbUypUIXLwmM0TFbKqJpZUTYe8ZCVD2a6V35caC/GgJVGirIOWC8Hs1q8YXUMZN11Ap663S5LV3owL1nGkhCIgatyyH1PXCuh4nvHhGTZEtCdJYSpn4eNF8Om37lvpHSkg/JLsCnAvSHITRF6+Yl4ppeRpS9u6FJ3dKtkPaj48AaDbqbAJBVoYlfu4u+EFQ1QVcC2E1PixpTwxf3gWyE1/9dxTz+xKH9PAYBKzrLvjnmW9C2WLNWELcmSgIVYKfOIsAHhFQowYk6NnQSusiJ6cDtaxaQBtrUQmb8gLuYSMCN7XlC2t0UA1UTIBpx7xFwr3WAbsgaSIyB9HJYfTvM+yJMPK1oH83BYEVn2TdVjXD4V+CthzTJOdXhziDv1mwTJ+p6IyPuTII2oEJDCb468DZqzdpkq3olidLTaqWBdsi2Q0JQR8wYCFZqbM/jA289ONtRseXW0cs9E8hWQOsLsLIDPLdBY+laPCs6y/4x7VIYexy0r4CutVrGPbpbPZbpmOvmT2gczySBqL5Hp3YlfRU6PvOPUydKqkPn9RGl5zjQABHIRiDuCtBb7Wa15JwqAXpmzsQgW6dLKHe+AituglN+CzWTivLRHChWdJb9w+vTCa81s7TbmGiF9legc6XOi4vuVm9mKqLLMDsJV3TuOC4Td62c33XEVIN/hq6lnoq4qWHd9CnA3Gqt+Nz3kqjp9KPWLgt06uqz6U7YsxJW3Ain3u2GK0qL0muRpbQRN6cyPEW3SWfplJ/OtdC2CiIbNHE63aZZJNm4u6Z4TNPCSKolTHbytiMmUA0VzZqvmcwJsJO9BZgu2Hd6He+GeJ0WSaIVtj8Ky/8ZFtxacjE8KzrLoeENQOUE3RpPV6dK+zrofBk612s9llSbdiedpFYSy8bV8pEC06XixAfizl4INYFnqlrMdAcaihioXGCOrZCdod1Rpw023Q2TzoCmdw3pR3CgWNFZBg+PH0JjYeI7oPEkFWB0C+xZppYwvlOXbk53aSJ0KuoWMkqgFjDnCfUDIa3HEpqgntBMQsVrOhlQgJk3QSYAPkhvhSWfg/c+A5WlkyBtRWcZGjxerQodGgNjjlSvZmwrtL4MXashulU9oelO7Xomo1r8NhPVOCBdrqXzoKGICk0N80xSkaZep9/SgWanXgMQXw3PXwtn/alkuplWdJahx+N1M1iOgNp5WiUsuh3aXoauNeoJjbfmBZiKuNN+Iq4AI3pNph0IajYLk4GB1pvP5l+2/AVW/wKO+sxQ/pb7jRWdpbiIRzNY6uaoNzQTg/guaFsJXa/oUs7R3RpOSEd1c1LqwTQpIAqpOOrNFPpf1isFhNHxIPDK9dB8KVSPL8IvOTBWdJbhQ0THbf4ZUD0dnHM1FNG2Sh0xkc0QbVFvZiYK6bi7KElE59XhJ79KbF/4gDFAO5CBRy6EDy0uxm82IFZ0ltKgMBRRNRkmnakC7HhFt8gGiORigd1uGCIO6RbyK8f2pgOoQb/mGXCWwKv3wrwrivZr9YUVnaX0yCU7hyfrNvFMdbp0roX2lTrJNrpLu6CpcbpPVz8368Kdvq68fCVMuwgqh2/1oJISnYh8GfgRMM4Y0zrc7bGUCN4AVE3UrfF0jd21vwbtL0P3BqiYBLufp/9Z7qbn60c/CJc+3s+5Q0/JiE5EpgDnAFv2da6ljPEGwDseJo6HxlPcYPyrMGYhrPspbztOBiL5BGx8GKZfMOTN7YtSqmX2E7RkQ2kUbbGUPm8H40+D+bfA8XeBb9r+XfuPD0Kyv7Hg0FISohORi4G3jDEr9+PcT4vIMhFZ1tLSUoTWWUYEHh8cdgW849dQ02c9oF4kYOGVQ96sviia6ETkSRFZ3cd2MfAN4Nv7cx9jzC+NMQuMMQvGjRs3tI22jDya3qOLpPia+jgY6rkb+SNsf64ozSqkaKIzxpxljDmy9wa8CUwHVorIJjTVYLmI9FUj02IZGBGYdDZMuwykt4cywV5f+Wcv0KpjRWTYu5fGmFeMMeONMc3GmGZgG3CcMWbnMDfNMlLxV8Dcz+ukWyrpETIg0OvkTnjuS8VrGyUgOotlSKiZAdOv0VkK+NFJr6DWrqbnuTvvgl2rita0khOda/FsjM5yaIjAtAth0nt1cZIeX/UIeRG6PHW+1twsAiUnOotl0AiEYc7noGYuau2C7oEs0Lt+yjZYsl++vEPGis4yuqmbC9M/CcGcp7va/bkNfMf1PHfj96DtzSFvkhWdZXTj8cCMy6DxDK2rSRod0xnIbAYm9jz/sfOHfMllKzrL6CdQq97M6tmoJzONejHboWoqPcd3r8HKnw9pc6zoLOVB/dEw43IINqBjuhDgg+hrED6j57lrb4DuXUPWFCs6S3ng8ULzR6DhVC37RxqN4aXAtAC9cjYfuXDomjJkd7ZYSo2KBvVmVje7b7gZKtFtMPEcegTOnaWw9r+HpBlWdJbyYvyJMO0j4K9Dx3deIA2RlVDfy7qt+BRE2we9CVZ0lvLC64eZH4eGE3VJLpKAD2LbYNw88M0sONmBxz886E2worOUH5UTYPbnXc+lB0jo2gsdK+Dwm+nhzYw/Dm8+PKiPt6KzlCcTToMpHwR/LW+vi9C9GeqmwfhLe5774rWQjA3ao63oLOWJLwizr4L6BagDJQmJbohugJN+ChTOLNuui5EMElZ0lvIlPAUOux7qjwGqdG30tnUQngDzb+t57sZ/g7bXB+WxJSM6Efm8iLwmImtE5AfD3R5LmTDpDJj3VRh/OlRM0KK3xsCcK2Ds+QUnxuAfX4Bstt9b7S8lUQ1MRN4DXAwcY4xJisjw1762lAcer04B8oeh5R8w7njN1wQ4+Q7462LAnWnW+STseA6a3nlojzy0Fg8anwG+b4xJAhhjdg9zeyzlxsR3w1E3alm/HLXNcFThdJ80rLv7kBOiS0V0c4DTRWSxiCwSkROGu0GWMkNErV5v5l0HtWfm93c+BbFDswmlUg3MB9QDJwNfBf4g0vdiYrYEn6Wo+Pxw8s+BOveNrbD5sUO65bBXAzPGPIgWI/qLUZagaeB9Lp1pS/BZis7YeXD4jfn9Fd86pNIOpdK9fAB4D4CIzEEDJ7ZOiqV0OPKLED7V3dkKGx856FuViuh+DcwQkdXA74ErjRni6bsWy4HgC8IJP+HtSmJb/nLwtxqcFh0axpgU8LHhbofFMiATT4BZ/wQb7gDn4DtiJSE6i2XEcMw3ILJa660kOiF04OvclUr30mIZGQTDcMTNWj06c3Dl2K2ls1gOlMaToP4I8FUd1OVWdBbLweAPH/SltntpsRQZKzqLpchY0VksRcaKzmIpMlZ0FkuRkZGcbSUiLcDmIXxEA+WZA1quvzcM3u8+zRjTZ0b+iBbdUCMiy4wxC4a7HcWmXH9vKM7vbruXFkuRsaKzWIqMFd3A/HK4GzBMlOvvDUX43e2YzmIpMtbSWSxFxopuAETkh24B3FUicr+I1O37qpGNiJwrIutEZIOI3DTc7SkWIjJFRJ4RkbVuweMbhuxZtnvZPyJyDvC0MSYjIrcDGGNu3MdlIxYR8QKvA2ejxaKWAh8xxqwd1oYVARGZCEw0xiwXkWrgJeCSofjdraUbAGPM48aYjLv7IjB5ONtTBE4ENhhj3nRLaPwerbw96jHG7DDGLHdfdwOvAk1D8Swruv3nk8Cjw92IIaYJ2Fqwv40h+uKVMiLSDMwHFg/F/ct+EquIPEnPdZFy3OzW5EREbgYywH3FbJul+IhIGPgz8AVjTNdQPKPsRWeMOWug4yLyCeAC4MwyKAv4FjClYH+y+15ZICJ+VHD3GWMOvsbevp4z+r9HB4+InAv8GHiXMWbU13AXER/qSDkTFdtS4KPGmDXD2rAi4Jbx/2+gzRjzhSF9lhVd/4jIBiAI7HHfetEYc90wNmnIEZHzgJ+iC2//2hjz3WFuUlEQkdOAvwOvoGX9Ab5hjDn4Us79PcuKzmIpLtZ7abEUGSs6i6XIWNFZLEXGis5iKTJWdBZLkbGis1iKjBWdxVJkrOjKFBE5U0TuHe52lCNWdOXLMcDLw92IcsSKrnw5BpggIn8TkS0iMmDit2XwsKIrX44BWowx7wRuAC4f5vaUDWU/tacccaewjAX+1X3LD3SISBVwF5ACnjXG2PmDQ4C1dOXJPGClMSaXTX80sBr4APAnY8w1wEXD1bjRjhVdeXIMsLJg/2hgFTppNVeuwSl2o8oFK7ry5BhUZDmORC3dNvLFl+x3Y4iw8+ksb+OO6e4AEsBzdkw3NFjRWSxFxnYhLJYiY0VnsRQZKzqLpchY0VksRcaKzmIpMlZ0FkuRsaKzWIqMFZ3FUmSs6CyWIvP/AVp8nFVIX59SAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(tot_s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stacked Neural ODEs with Discrete State Transitions\n",
    "\n",
    "These are basically the `Stacked` model where, at the end of an interval $[s_i, s_{i+1}]$, the state is also updated by learned transition maps $g(h, \\omega_i)$ parametrized by a NN, i.e.\n",
    "\n",
    "$$\n",
    "  \\left\\{\n",
    "        \\begin{aligned}\n",
    "             \\dot z &=  f(z(s),\\theta_i) \\quad s\\in[s_i,s_{i+1}]\\\\\n",
    "             z^+ &= g(z(s),\\omega_i) \\quad s = s_{i+1}\n",
    "        \\end{aligned}\n",
    "  \\right.\n",
    "$$\n",
    "\n",
    "**NOTE:** While not standard, this class highlights how Neural ODE variants can be put together hassle-free via torchdyn's API.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We choose to divide the domain [0,1] in num_pieces=5 intervals\n",
    "num_pieces = 5\n",
    "\n",
    "# stacked depth-invariant Neural ODEs\n",
    "nde = []\n",
    "for i in range(num_pieces):\n",
    "    nde.append(NeuralDE(nn.Sequential(DataControl(),\n",
    "                                      nn.Linear(4, 4), \n",
    "                                      nn.Tanh(), \n",
    "                                      nn.Linear(4, 2)), solver='dopri5'))\n",
    "    # In this case the state \"jump\" is parametrized by a simple linear layer\n",
    "    nde.append(\n",
    "        nn.Linear(2, 2)\n",
    "    )\n",
    "    \n",
    "model = nn.Sequential(*nde).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type       | Params\n",
      "-------------------------------------\n",
      "0 | model | Sequential | 180   \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dfb490dae0e64eedb4aae83900684029",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jyp/michael_dev/testenv/lib/python3.7/site-packages/pytorch_lightning/utilities/distributed.py:25: UserWarning: Detected KeyboardInterrupt, attempting graceful shutdown...\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=200, max_epochs=250)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Evaluate the data trajectories\n",
    "s_span = torch.linspace(0,1,20)\n",
    "trajectory = [model[0].trajectory(X_train, s_span)]\n",
    "i = 2\n",
    "c = 0\n",
    "while c < num_pieces-1:\n",
    "    x0 = model[i-1](trajectory[c][-1,:,:])\n",
    "    trajectory.append(\n",
    "        model[i].trajectory(x0, s_span))\n",
    "    i += 2\n",
    "    c += 1\n",
    "                      \n",
    "trajectory = torch.cat(trajectory, 0).detach().cpu() \n",
    "tot_s_span = torch.linspace(0, 5, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(tot_s_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WgCkdrPDthcrKStra2nDH0NVisUwqejab/LzWF2HjA6BeG6KhR/8lJ4W5IQ8wotcb1OKVQVQAqcGpgEQ90q2AjpcQ6eNG/1iGYNclkIoCaOf/Jif2ar4XXNcd8Rwii6UkUBF0vWaKTO94GZp+hWDHEI2L83kOJmoTjGtTAQlwEyDioHLg+Ggvg4jPQCfrwJuO2/0qQv3dGBzUnrEVYEoDK3wWi2XfifKI9j8jm1cjtjwD7Q9gXJa7MjA/z8MIIPRZejIJJEH6oLMg42i3EpGahYrXI/xKhBsncipw8tsgNnNMDm9v2ACYyY0VvmHgeR6FQmHMJ9YtlglJvg3Z/rypt7npD5B7fIiGHv3zeTGM6BXFUZv5PDdt/iYPMg3JaYhYPTregPRT4JYRxaYjghw0/xEy5+z3en2jwWAVYDzPs9bfBKckb0+iKGLJkiWceuqpI9JfdXU1LS1DhWRbLFOIbBNy++OIbf+D+NudexA9H3N50Zj8PAcjeqr3/TT45RBFQAhuOSQbID4LlZoNsRQ6Vk0Ub0DqHFJ1IrWC7o1jcZT7xMAgtyiKyOVyBEFgp0gmMCVp8V177bUsWLCAjo6h6gEOj56eHnbsMHMWDzzwAMlkkg996EOjWj3CYpmQKAVdr+O0Pgs7XoKme4BtQzSOYcRNUqy9aebztHntpoA4RDlwHbRTjUhMh2QD2q9DuDF0bDraK0cGLWhAizg4PhRagNmjf7z7gQ2AmTyUnMW3efNmHnjgAS6++OL97uN//ud/WLZsGSeddBJf+MIX2LhxI0899RTNzc1E0WB1Bi2WEibKI9pexNn2GGLjo4immxBDil4Cc1lxMZGb0LfWnoyDVw4iBiILMob2ahHp2ejUHHRsOiKWRiVngpdEFrYBDggX7aXQyTngV0LQNcoHfGAMLMgeBAH5fJ4wDK0FOIEoOYvvi1/8Iv/xH/9BZ2fnfvdx/PHH89xzz/W9/uY3v8m8efM4/fTTR2KIFsvkIehAtj6PaPkTYvMfILtqiIYuxr0ZYYJZPEweXi8iASJtlieSBfN3ohoRb0DHGxF+CtwMUaIeqZSx7GQapEa45ShvOsLPQNgBTszk+k1wbADMxKWkvoH777+furo6li1bNqL92jk+y5Qk+zZy6yrktkcRf/vVHkTPxwgdGIvPw7g2I0CCSKFj5SY3T0bglJn5vORcVGoe+Gnwa4jiM5CqgA7a0E4SBGi/lih1EEJIk+oQq4UwB7nW0T/+EaIogMUAmEKhYK2/caakLL4nn3yS3/zmN6xcuZJcLkdHRwcXXnght9xyywH1W1NTw1/+8pcRGqXFMjkQrS8i3/4dbLmXodfPczGBK2AsPehPSo+BkwQZR0R5kA7IKkhNh/h0VGwGwnXRfh3KK0eGHWgitJNECg8dm45KNCBUlxEKvxZyzdD+IngZaDh9QkV47glbAWZiUVIW31VXXcXmzZtZv349t99+O+9973sPWPTAWHytrZPnDtNiGQm0XwtbfsHQogfGsgt6/873PgLAAZkAXJOfJxy0XwOpWejkHHRiJtJPoBKzwCtHBs0mBkb6SDeJSs1GJxqQUQdKxNBuJXSvg5Znjbs03ghqsLzBic3ACNAwDO383zhRUhbfaGFdnZYpSeViIsI+e25oQnYuRt1bpUV1YwJb4uhEOSI1G52oB68c4SSJko1mPi/YZtyhQiC8cqJ4I8JNIqIOtFsOuMiOl5FqOzhpqDwCkjNAjn3tzpHCVoAZX0rK4hvIe97zHu6///4R6csKn2VK4jho/8z92LEAdAKtQDvQglAeKjUX/EqEX4VKzkSqAkRtaDcDUkKslih1MML1EVEP2q8GrRBtzyCzm8z8XvXRkJ4DwoHc1klp9Q1k1wjQQqEwrBVfLAdGyQrfSGKFzzJl+cDPiIZe3WWYBKj8OoSbBL+OyK9FhN3ooActTXK7jjegknMROgcqQvm1UOhAtDyNLLShEnOh+igTFBPlIWg3Zc5EaTitbADM2GKFbxgkk0lyudx4D8NiGRd0w1cOuA+Jg040mqT0sA2URnsxhJNAJ2ehE43IqNPk9vmViNwGZNtqhI6IMoehyw+DWI1JZ4h6TKmzWDWI0rmE2QowY0fp/GpGGfvjs0xZln2JiFkH1EXknQQyhig0g/DRjkA65b3uz+q++TztJBEdr+K0vYKWcVTlMnRmvoniLDSDCkwSu1fW37kuraISNgBm9LHCN0yKbgiLZSqiD/kSsP9J47J+OSJoRjsJQCD8GqL0QSB9RNRt5vMQyLY/4fRsQMWq0ZVHo1Oz0cJFFHqnGmI14CT6Ow46ILfNCGKJYSvAjB4lJ3y5XI6jjjqKI488kkWLFvG1r31tRPotKytj48aNrFu3bkT6s1gmFYd+lMht2O/ddVkM7WRAuujEDJOUTgC6OJ/XiWh5CpFrIUrMQle+00SAqgKiOJ8Xq+2P5NQK8s0QdoGbLJm5vsGwATAjj9jL3cOku7XQWtPd3U06nSYIAt71rndx7bXXcswxx+xTP6tWreKKK66gtbUVrTXr1q1j/vz5zJ49m5/+9Kc25Ngy9VhzPe66bwI9+7Sbpgy15L+Qwkcl6sGvM0npMoZ2KxDZTcjOV0AJVNkhkDoI7ZUbwdMFQuJoN0MymTQdqsCUNNPK1P50kyN/rBMUrXWfxWcT4PfKkCem5G6ThBCk08YlEwQBQRDs1w/jne98J3fccQeVlZVIKfnUpz7Fueeey/Lly0d6yBbL5GDR/yHaeh9Oz/PA8IO9NNOQThqVaAQ3PWA+L4bofAWnax3KTaErD0MnZ4BMIAIjbNqrAPz+K1iUhUKbCWqJVRtLcAqx6woQxfw/K4D7Rsm5OsGsx7d48WLq6uo48cQTOfroo/e5j3Q6TXV1dZ+LwaY0WKY8QqBn/W9wMvTX5hSwlxR3kaw283lO3MznedWAg2x9Dqd7fe983nJ0ao6Z8wvM/5n2q8FJ9M9pBR1QaDXuzljtlBO9gdgAmAOjJIXPcRxefPFFNm/ezOrVq1mzZs0B92mFz2IBZp9FVLEcRCWmNqeLKUY9NFFiAYIIdICK1UDQg2j5IzK3nSjRaEQv0QA6QARtaOmZ8mYD5vNEoaV3Pi8FfmmlMRwIgwXARFFkBXAvlPSvp6KighNOOIEHH3zwgPuqra21wmex+D76oC9AzdHgz6C/TudQCGTFOwAH7dcisluQ7c8gojxR+QKoWIKO1UDUZaq1OMmdhU0FiMIOhA7Aq+hdz8+69HZloAAWCgUbALMXSk74tm/fTltbGwDZbJaHH36Yd7zjHQfcry1UbbH0Uvd3hDUnQCHce1sS6NR0tJdBdP4Vp+1FtHBRlUvRmUPRbgYRtCJUYObzvPL+XcMeRKHZBHT41VMqiGV/2bUCjE2AH5ySC27ZsmULH/nIR4iiCKUU55xzDqeeeuoB92tdnRZLLzpCdrcAG4bROA2xucjWF5D5rahYFbrsCHR8GoCZzxPSCFufa1ND2GEsQOmj/cpJXZB6rLEBMHun5ITviCOO4IUXXhjxfq3FZ7EASiGafovceMUwGsfR6fmI7jVIGRIlG6HsMLRfBSrXJ2x4lf2uTa0QhVbQBbSTAq8MXSjYC/Z+sKsAFtcAtCtAlKDwjRbW4rNYgOancV64YBgNPXCnI9w4SEVUdiikD0F7ZYigYydh60MVEEFbfxpDb4WW4gXcsn/sugRSUQCLUaFTESt8w6SiooL29vbxHobFMn60/wX36bOH0dADKsBNo5Iz0VXL0MlGsxJ70LqbsAEQdiPCzt3dnpYRY6AAFgoFpJR4ntcXFDOVsMI3TKSUdpLYMnXpfgv3D3+PWWdvT7hAGrwE+FWQfgc6NRfAiN6g83ntiCi7u9uTYhP7fzeSFK28YgDMVJz/K0mp37RpEyeccAILFy5k0aJFXHvttSPWt1KKjo6OEevPYpnw5FtxHr0IeHMvDeMgqk1yebwWUvXoeJXJzwvbB8nPixCFZiN6bnrI/LypdEEeK3ZNgJ9qSyCVXK1OMJGdW7ZsYenSpXR2drJs2TJ+/etfs3Dhwn3q5+GHH+anP/0p27dvp7W1lbVr1zJ//nwOOeQQfvKTn4zS6C2WCUSYQ/7hS8jun++lYQrcSvBqIDHNpCVkDibKLIKaZbvP50V5M5+H7nV7xofsOQgCfN/H86z7c7Qo1gAVQpRSAMzUqdUJUF9fT319PQCZTIYFCxbw1ltv7bPwHXHEEVx++eXU1dVRUVHBaaedxve+9z0aGva/Sr3FMmlQIfLl6/YiegKoMmvkuRnwq9B+OSI2A+1lIF47yHxeV+98nov2KkHu/TJUAhfhCc1UC4ApSeEbyPr163nhhRf2q17ntGnTmDZtWt/rYmSnFT5LyaMUbL4f+dbe0haqILMQHatDRGY1BYFCCYFIzEDH6/pFTysI2hAqj5ZxU4llGBfVqeJ+mwhMlQCYkha+rq4uPvzhD3PNNddQVla29x32QnV1Nc3NzSMwMotlgrPjj7gv/e+9NKqCssNQmXlIL4MWjaBAhB3IqBPVsxGRmGXmS1TQm6oQot0yU3PTMmEZGAAThiG+X1oFwUtW+IIg4MMf/jAXXHABH/rQh0akT5vLZ5kStP0F95m9VTuqgrLD0Zm5SDeJdjPoRD3CLUdpDdlNSJ0n6l4H5e8wa+sheiM69/0iWorutolO0forNWsPSlT4tNZcdNFFLFiwgEsuuWTE+rXCZyl5urfg/s+pwJ4KHFdC5jCzjJATh0QtOjEHYvWosBXZ/SYi6iZKzUWXvcNYesJH+xUg9ryEkcUyFpSelANPPvkkN998M48++iiLFy9m8eLFrFy58oD7rampsWXLLKVLvgPn0bOB7XtoVAFlR0B6JvgJRKKRKHkwJGaiC804PRsBUOWLEKm5COminZQpU2ZFb1JSitZ2SVp873rXu0ZlQtxafJaSJcojH/ssgpf30Kgcyg+HVKNJT0jOQaUPQogkdL2OEzSjYnXo9CKQIHSEdndJY9hPSvHiaxk/SlL4RgsrfJaSRCnEc/+JDO7dQ6MyyBwOid40heQ8dNkhEOYQPa+AiIgyh6HLDkUE7QhdQMUbTCK7ZVJTijcdVvj2ASt8lpJkw704W6/aQ4M0ZI6AZD14lej0IZCci85uwylsQ7lpdMVyiFeZUPhYHegQQYgOuw84gtOmM1hGGit8+4AVPkvJse1p3DUf2UODFKQPg9R08Kejyw8Bbxp0v4GjskSJ2ejywxFuAqRrUhWcODrsQYTtiLDDrKq+n1aDXUV8/ClFi68kg1sAPv7xj1NXV8dhhx02Yn3G43Hy+TwdHR1s3bp1xPq1WMaF9tdxnzlpDw2SRvSS9RCfgapciJZpRPZ1hA6IypZA1VKEl0S7KbRfCwhEfgcibO+vzHKAF85SDam3jB8T5teklEIpNWJujY9+9KM8+OCDB9zPbbfdxsknn8zy5ctZunQpr732Gueddx4/+tGPRmCUFss40bMN9w/v3UODOCTfAYkGSM5GZQ6DMETm1qOdNFH1cVA2z1h3fjU4KQhazYrqKLRbjo7V7rEGp2VyUIoW37gWqX7mmWcoLy9n9uzZJBKJve+wj6xfv55TTz2VNWvW7Hcf27dvJ4oiampqcF2XZcuW8cgjj+A4NjTbMkkJczi/PQHBK0M08CB5GKRmQ3oeKv0OCJqROkeUnA1lR4KfNi5MJw1RFyLqAYRZZcFJHbCVV6RYOSSdTo9If5Z9Qwgxmau2TMwi1b/73e/o7u4mDEM2bNhAPB6noaGBuXPncuihh3L88cePe0X22tqdo9IqKytpa2ujurp6nEZksRwgf/zmHkTPRScWIJKN6MxB6MQ8RGET4BKVHQ5lh4KTQLvlJoClsANQRgTdzKDLClkmL6Vo7cE4C9/555/Phg0baGlp4aijjuKxxx6jo6ODjo4OfvCDHzBv3jzmzJkznkPcjWKAixU+y6Sl/f8NscFBxxcg0rPQZQvAq0Pmm1BuBl21DJKNvVZewqyuoAOzeKxbNqorppfqxdcyfoyb8GmtmT9/PvPnz+9779xzz+Vzn/scy5cv59JLL52QYcw2stMyqWluZnAnvQT/EETZXHT6HeAmEVELUXwaVC43ywu5abOobNAKwtl9uaFRYCJeA1gothwAACAASURBVKYSpXrTMW7CJ4TgoYce4qWXXmLWrFnU1tayZMkSXnzxRY455hiAvoURJxJW+CyTmqe+MPjEh3cQlB+ETh2Klg5S5YmS86HynehYGQgfEXYB2lRtcTMjNo9nsYw14yJ8URThOA5NTU2sXbuWzs5OCoUCt912G0cffTTHHXccwAGFMP/93/89q1atYseOHTQ2NvL1r3+diy666IDHboXPMqnRj+3+njMXKg9FJw8FFAIHVbEYyheinTRCR6C6TKFpr3xYC8eOJBPt5ncqUarnflyjOos0NTWxdetW8vk8hxxyCFVVVWPxsfvFLbfcwqZNm/jc5z433kOxWPYZcV/Z7q7Oivehyg5DSlDxGnTlMZCajXY8hCoAEu1mwE2O+XijKAIYlahvy95xXXcyR7APqdrjFoLV1NTE66+/DkBDQwM1NTW0tLRQVVU1of361uKzTFo2Pjr4/J5WSAeixAx07YnozFwQAqEKaCdh8vHGQfTAzvGNN6Vq8Y25q7M4b7dmzRq+//3vc9FFF7Flyxb++Mc/UldXx8knn4xSasLeZdhV2C2TlteuH/z99rWohtNg2vvRXty4NoWDdqvAiY3tGC2WMWDcLL6qqiq2bdtGc3MziUSCs88+m8985jMAIyp6Dz74IIceeijz58/n29/+9gH3V11dbdfks0xOsmuH2NCEjteB6yF6g1e0XzthRK9UrY7JQKme+zG3+Ion8uCDD+baa6/l6KOPHrXPiqKIz372szz88MM0NjayfPlyTj/9dBYuXLjf/Sml2LRpE6tWraKiooLFixeP8KgtllEginAoDLlZNj2Bql5uyo/JiVOpw7o6LaPBuFl85eXlHH300X1iorUe8R/56tWrmT9/PvPmzcP3fc477zzuvXdPa44Nzle/+lWWLl3K0Ucfzec//3nefPNNfv/737Nly5YRHa/FMmp0vIZwh7bgxNZ70FFhQomeZfyxFt8ooLUe1bm8t956i5kzZ/a9bmxs5Jlnntnnfr7xjW/wjW98o+/1kiVLuOKKK0ZkjBbLmNC9eS+3uVsRbc+j07PHakTDYiLm8k4VSvm8j2thvcl8Yq0LxjKZEF0vgfCAoReFla/+AoLOsRvUMBBCTOrrhGViUtIVZWfMmMGmTZv6Xm/evJkZM2YccL/JZJKenp4D7scCWkMQmGfLKKEik48XqwW3fshmIv8gdPxlDAdmmciU8g1HSa/Avnz5cl5//XXWrVvHjBkzuP3227ntttsOuN9iLl8qNfTds2V3iiLX0wOtrdDcLNixA1pbJQsWRNg4oVFC5SE+DfxyiAIIU0D3oE3l5lWoyqVjXp1lKKxnxTIaTIxf9yjhui7f//73+cAHPkAURXz84x9n0aJFB9xvUfgGzh9adqYoct3dRuRaWgTbtkFzs0NzM3R2mm3FNi+95LJoUcg4r0JVokTo1HyI/RmiAmSrQA0hfBt/hjro7yE9MX7bpWx1THRK+dyXtPABnHzyyZx88skj2qet3rIzu4pcc7MRuZYWh+3bzftdXRCGoJSpbSwlCKHxPOjqErzxBjz/PIxidsvURcYh2YBKTEPktyL8asg1AdEgjTch2p9HTxDhg9K+AFvGh5IXvtFgKgtfUeSyWWhu3tmS27HDCFxXF0SReQgBrmtcVp4HUSQIAk2hINBaUCgY1+fmzfCrX0mOOkrZov8jjfTAy6CTs5E968Avg1wFMHgFIvnXO4nq3gteZmzHOQRW+MaHUj7vVvj2g6kifEWRy+X6RW77dti+3bgru7qMy3KgJWeyUzSua/5xwlDT0yMAQT5fDGQx/1BhaPbR2liFTzwhWbdOMW/eeB51aaLdFCI9H9pfBK8VvEoIBhc+0fMAdKyF6neO8Sh3x87xWUYDK3z7QU1NzU7RoqWA1kaIcjloaTEit3WrCTzZvl3Q0WGErhiBqbUROSn7LTmlNNlsv8gZQRRobYSx+DlFV6fjmEcyafp96y24+27Bl75kL3YjjkxAvAYVb0B2vwWxSghiQH6QxhFy25OoyiUgJ2bNXMvoYy2+EuHOO+/k8ssv5y9/+QurV6/mne/cvzvaUrD4whAKhZ3n5Jqbjci1t2u6uwVBYASpKFKg8f1+N2ahIHpdl6ZdUeQGPoTYWejAPHtev0UppXnd2QkrVzpcfHFIRcV4np0SRLrgpCE5G7regLATqATeHrz5Gz9GzfwwpBvHdJiDUcoXYMv4MKWE77DDDuPuu+/mU5/61D7v++abb7Jx40a2bt3KSy+9xKpVq/j85z/PBz7wAU499dRRGO3IEUWQzxth2bEDtm8X7Ngh2bpV0NFhRC6fN+0AXFcghMZxNFIKgkCQzZoLUKFgBLNowQ187g9aodfVaUTOzPEZkQtDM5ZczvxdFEgwr998E+6/Hy68cOzPU6mj3SSk5qG9PyH8FCSqIbsNUIO03oDoeBE9AYTPMj6U8g3HlBK+BQsW7Pe+v/zlL9m2bRt1dXXU1dURi8X42Mc+xpw5c0ZugCOE1sZduWNH0ZoTbNsmaW3VdHUNdEOC44g+l6WUEIYCk5tvBK/QW9dYqX6RK35G0ZpznJ1FTqmiRWgEbqDIFXf2fE3M1/geJJOat2ok7e2S9nb45R2a8z7UihtLghMf47NXwjgJ8MvQiUZEtgmcSiAJdA3aXP7lDqLa94CXHstRWiyjzpQSvgPhy1/+ct/fhUKB2267jaVLl47jiIampwd+9jOHjg4jYlHUPycnUIighVjX6wRBgXyUApEmIEU+8kE7aOESKYlGIoURMlm05tAgIjyhcT2FViFhHgKlyQWQzzlECiKFMSSiAM+LiDkRvhOQjvcQ9wOELoAOiZQmbBXU+GX8jcOIIsGa53v44w3fZsWKLHrxf4Fjf6YjgnDAyUBiDrhrwe8w4hcNLnyi5wHofA2qxvd3XsqWx0SmlM97yV1R3v/+9/P227vPW1x55ZV88IMfHJHP8H2fIAhGpK/RIJWCtjYTaOI4Gscx82+5nEB1v43a/gKFnnZCjKppfLRWoBVauqAEUkik0AipEBI8J0QCYeQSRg750KW1kCRUPhqFUqCR+G6OmBPiyYBUopNEIo8kQimN0g5Bt0uuUxIqFykgjBy0hkqnGZgPJGjtTPLj+5fz3oMvJqz+AMyZYK7koBOybRDlAQ1I0BGI3gqASpi3owhQve8LIzwII+RiQNCIcEC4ZpvsNZ+h36RGsFuOh5Q73xDssj2KTKSs6wn8mMDtbaqdOKRmor0qyDcjvGqItgDhIAcaIrc+hao40ga5TDFKWfSgBIXv97///XgPYUKQyWhaWnRf8EkUYYStdQd0FkC4aBWhhYsQGqRAEuE4Ib4M0FKhQpdC6KGUR0dXmkC7aCVRSpr5PBEQc3vw3BzJWJZkLIcUEZECrSWB8skWXMIohpSSMHBQQKgljjBjixCgXJTw8OgiIEmE5Km1K/jrplnMl18df+FTCoI22PYi8rXrET1PIpjYtVoL+QS5nv4IISkUvlsg5ubx3QKOO5jQ7Y5843bUvHNMnc9xwKYzjA9W+CyD4jgOYRjiuhPzFDqOprNTGEusdz6OQjeyeysIcCVIqfDdLEIqokiSC2MEoUtnIUMhiqMik2SuhMQTAXE3Qvo9pGLdJPw8jghAaLRyKUQePYU4KIESLlHooLQgVBJHKsK8QOGAdggijyhyUVr3Gioaz42YUbGV9W11gGBHZy0/fPgTfO/j/5coDGGsz7MKILsD3rwTuf4mJG+M7ecfIO3dabrzSRoqmxACCqFPPoyRC8ycqRSKmJcn5uaJeXkcuXuAiwJU1XvALR/bwRc/Xw0WdGOxHDgT86o9Stxzzz18/vOfZ/v27ZxyyiksXryY3/3ud/vVV1VVFa2trdTWjs+d8N6oquoXvGL9S1d14iZ60FFEIfQJiNPZU0W+IIiUREhNqB08Ajy3gOspUoluYl4WjwAhNUp7BJFDruCBjhEJDxVJtIZIOYAmjAQaidZur2vUQ/UFw2g8NyDu5vCcCN/JIx1NEHg0Vm9lfdsCwCcC7nvuQ1x25rcof+V6OPIfR/+kBd3Q9hri1f+H7PgdgvFdoqdo7BQT/jVip9dKmRubMDJzspGWFAoebdlKnnr9WOJuwOzaDcypW09NZgcVqXYiJckHMfJhjHwQI1tIAOA6Ab6bx/dz+O5sOPTf4ZCzxv6gd0EIgZQlvYjMhMRafCXEmWeeyZlnnjkifRVz+Saq8B18MKxe3eulK6YRNO8g11VuAle0ACSRECTcLD49pOOdJP0cnldA9ZYbC5VHvuASap9Ae2gcdKSJtARt3JZaA9qhEPmEoYfCrHclRITjRsRjOTwR4XoFJJogihNELl25MrJBglw+RoRHoFxMQrUPCLa0NfLTxz7CP1V+fXSETynIN8PffmmsOr12v7r5W1M9r729kCB0CAKXntAlSJxE4FUQhIJ84BNEkrBHEkSSbOAShi65yCFfcAhykmzgkCv45PMOPTlJLu8SKkEQuuTyHl2dgnzBo4AAHMwZLj7MRaoiEzGtOk9jfSdl6ZA5DZ20ZLvZmstSES9Qm8kyraaH8rIQ33HIOBkCbwZ5WU9eTKMzNPN4UkIsponnIBbbfXrRYpnsTCnhG0kmehL7/PmwbZsRvGJ+ns6miDlZYr4mHiuQ9LPE4gFaKWShnTAKCEKPXJhAaVDKRWtJpJWxHjUEyjGWnPLJBW7fZVgLjeuExGNZPBnheSaoJVdIEiqXzjBDrjNJdyFGpGJESiCQOI7C80JSfhcxt0Cup8CbzYsw8acOP3v8k3zh1BtwlDJX5AMlyMLWZ+HV/8TJP4GgsN9dfeuWI7nit/cDGfr/lXqDUcaB9i5wYynKwirmzwOZ1rT6glxOk+nW7PBhsxBURIrp0zW1tUbYPCANKKX7cixzuWLuphHBRMKK4FTCWnyWQZnowjdtGqTTiu5uSTIJ6bQmUbYFUWhDaAiR9GQ9WreV4ToaESVQutskossIQa/wISgEcQIdM743JUAqPDciFQvx3AjXCREoCoFHGPm05xJk2xPkwhhKeUShQKBxnJB4LCDu7EA6iphn9ouUawJh8h5l6QCaQ8zlWLB+x0Hc89TJnFXxWXjff+/7iVAhtG2Gv1yLbLkHyYF/Z0pB+h/+BCw84L5GEq1N+TffN+XlUikzNZrPawoFSU8PZDKKri6zckY6ramrM49MxtxXJBLmobWmUDDFyPN5QS5nRC8e7xdBi2WyMuWE71/+5V+477778H2fgw46iBtvvJGK/aiPNdGFD+DYYxV//rNEa0VQEGSzkiifNHNDWpILfdZtmY4jQ1Nzk260VAgtQUQ4ElwZ4rkK34twpLEUHUdQUB5h3qMtmyAXxMjlPSIlUZGDIMJxIhKxHDGnBykjPDdERRAojyA0+zaHSQraQ0UgEWgHnChEsh1FAwAKl/9a+a+ctWIFMAzh0xoK7fDqDxGbb0ayYYTtL4cNm8o5cNHT+/j3rgz+r9vaCtXV8Pbb0NYmqKvTNDRAPA5hqGhpkXR1acrKNNmsqdrT1CSorNRMn66pquovSBCLmcdAESxagkYkjQiO5hqKpW55TFRK/bxPOeE78cQTueqqq3Bdl0svvZSrrrqKq6++ep/7qamp4Y033mDHjh0kEokJuRr7IYfA009DFEnCUEM2CUoSRRLh+HT2xNnc2kCkBI7USBHiySwxt4DvRyS9PI6TR4ZATqGVJNAeUegSaePkFDrCdxV+LCDu5om7eRxHEYaaQuiSDXzyYYJc4Pe6TjVaS6SIcJwAVxaQnkASoolwfMkh05v569t1FH+er2xezOpXFnHUaUMcaKEHXr8F1v0QqV9jZEMhXCAJTjl45Wgvw9wlFVTEttCWr9+tdXl5yOc/DzNnQlkZVFZCfb0RnspKY42NhMe2vj6ku3v3f9/OTiN+vm8s06YmQVubYNo0zfTpxiJUStPWZgSwokJTXq4JAkFLiySd1kyfrqip6bfqdhXBfN4USejpEXR3G+EriuBIxqHYVAbLaCH28uMq6V/ePffcw1133cWtt946rPaXXHIJr776Kjt27KCtrY3Ozk4WLVrEZZddxlFHHTXKo9138nn45CcdslkT/Vfo3I4KCig8pHTpzsZ4Y2Oqb908FYbosIcokmgp0aEAKRBS4KAQIsJzIpML5ueIOQF+LAQtUJFCK4cCsd5UBYmQEqU0rizgSI1AgdBIHYDjoENwXIXAVIYRMsKVxnX6/Lo6oF9Yjjvo9/z2Gx+F09ZDmIPXboM3/xup146w0PlAGXgV4JWBXwnxKpBlEK9FxaeBX472K/m7U5ay5rXdg5vOPjviJz8Z3X+d556DE07oTYjf9Qh8qK01j4oKI7qOA+k0TJummTZNk0pJwlARBAIpoapK9wqzRghJImHa1dZqksnBx6CUsQKzWZMrWpwPTKXMGA6UKIpQSk3Im8pSx/f9UrD6hjyAKS18p512Gueeey4XDrMi8uuvv055eTnV1dW88MILXH/99Vx33XWjPMoD4//+X3jpJRelIOZGuL7CcSS+L2jaIli7VvSVNAtD0FEerTRaSdCa0CQm9PVn5MsEcBQFRwqNI0wpM6kjpBsRcwEChCNwRITrmAImvqOQjkKKAF8EuH4BX+ZNhRkihDTJ760dPq9uWUTR6pMErPneLGZNbx9BoROYsI5yiFeah1MOsRp0fBo6VgfxarRXAX4NOl4FTgqcGAgPpMtZZ8FDD+0uQNddF/LRj47YQAfl2GNhzZrBnTaua+b4amrMo7xc4/umgksmAw0NmpoaTSIhiSLVW+UHqqs11dXgupooksRi/fOA6fTQwS1BYKzAXM7cZLmuqcF6IFZgFEVorUkOpbyWUcMK3yRkOGXLrrzySv70pz9x991379cXvG7dOr74xS9yyy23HPB4R5Nnn4Xvf9/pXWtP7FQ42qzUsPMyQlrlcUSE01ujM9JAb+ymQvbmkhV/FsUIRkX/b6y43TxcAhwiXC/EdQJcAa6nTbUYJMLRCA2Oo3CcCKF7P0VHvLG9FiNMpu9TjriNOy+9+ADORhwwLktSNSCrIF6DTk5HxxvQsUrwaozw+RXgJEH6ZgVz0X/1Vqo/WjYM4dJL4ZZbdhU/zdNPRywcxfiXri5oaCimNAxOImFcrrW1RgDT6f5i4pWVZv6vutq4MaNIk8+bpaUqK43YeZ4JbonFoLbWWIBlZUMLoNb9VmCh0B8Qk07vew2CqDccOZFI7NuOlgPGCl8JctNNN/GDH/yARx55ZL/vJjs6OjjllFNYuXLlCI9u5PnUpwQvveQMWJHBXIS2bTOrOLhu/xp7WkeYr71Ym1HTL2a7il7xWe2yXe7ShgH7acDUsJQoPCL8WEjMCfG9AEcWoz9DNm6rpCdIYyI8AQq0/KSC+LAWbHCAMhDVkKkBvw78anRqBjpej/ZrjcDFasHLgJswVpwwkR3F8xGG/Y9cTtDZaSybzk7zMKvQS+67Dx57bNdjjmhu1qMa/PGFL8BNN+1ZUaQ0gldRYaJ9q6vNa63N/FxtrWbaNFP0wCwqrOnpEQhhLMCaGrMOY6Fg3KLV1UYUy8v3bM0FgakXmssZMfV94wYd3vcHYRgihLDCN8YIIfBHwlc9/ljhK/Lggw9yySWX8Pjjjx9Q8rnWmqVLl/KHP/xhBEc3OjzwAHzvey5hCJ5nAhm6uszad6NfFWpXodxTO7OkgxQaD0Vea4rJ7EUx/ejxV/P/ffrrg+xfCaIGMtMgUWcsOL8Bna43bspYNcTqzNI8TgyNR6TETpabWbPQBGwUV5zv6DDRkV1dolfwzGr07e1G+IouvkIBNm0y7w2koiJk48YDOH3DoKpKEIZ7LyIdixnrr6oK6urMc6w3SyWRgPp6k9tXVmZ+J0qZ4wWoqzPWnuMYC1AIqKkx7+1NAJXqD4aJon43aDK557xAK3zjgxW+EhS++fPnk8/nqa6uBuCYY47hhhtu2K++lixZMimEL4rge9+Dm2926ekxF+vOzv7E9tFhoIU31O9vV2ty1/eKlufA7YqeW9PAoVAxA2LTUclGdGoWxHtFLl4LfhmRjhFpjzCSRJFx73Z1GdFvbzePjg7o6DCRj52d5u+WFnOh7uoyYpjNGmELAvM80Aoc6PYc6ibiggtC/ns/UhCHy29+AxdeOHw/4kDrr6rKuDUdx8zNlZcbAayu1qRSAtfVBIE5b65rxG7aNLN2Y09PvwU4HAHUuvgd6F43qO4VQNPfrtcirTVSSmKxGI5jV4cYK6SUeKPpphg7rPCNBkuWLOHxxx+fFL7wpib49KcdXnhB0N6+t9bFK3hETAZ4MsDzQuKJiLiTx3EiYr7J/XOkMhd9DUI4hKEgjDxC4aBDSaAcwsAhCh0CIVGhi4okCmNt9c8GFkNoBlY+6bf0BvLJ917B9358ApFXR+RUEokEoXLJ5pxeK03Q1maEzTwbYWtpEX3vdXaai3BPjxG3IOh/LopYFJnXB47itdcU06ePRF+Dc8QRsH798MXP84z4VVf3B8CkUhqlzLmvrdXU15tIz0TCLG9VKBi3ru+bY6mpMd9YV5dACEVVlXGBlpUVv9X+QtO7/o8UCtDdLcjnBY4jSCY16bQR0mJtTiEESimUUjiOg+u6tm7nGGCFzwrfHjn++OO54447yGQy4z2UYbFtG/z7v0see0yyfXt/5F8mYy50M2ZoZs7UHJxaybyaN6mpaKUy00XK6yLh5vDdAOmECGkCKqQ0OXlaO2gVERRC8nlNPnLI52PkIlOHs6M7SXchQVc2Tnc2RltHirbOBDs6MnRkU3Rmk/RkU3T1uGSDGPmcTz5wyRU8mrvTGHfnQAJ+9StJW5vJWWttFbz9thG2oouyu9tYakU3ZDbbvyBvEAxYDX7MCOnoGMXeQzjtNHjyyX2LIEmnTX5hVVW/CMbjmjA0Fl5Dg6auTpnKPwkBRPT0GNEy7lFFZaWZF+zulriuiQo1AiiQ0lx7hBB9D+gXt6L3IZ83Vn4qZcY0UN+UUn2BLp7nWetvlCneZJQAVvhGgzPOOIMrrriC2bNnj/dQhk1nJzz+uBGCOXNMonVFxYDEaq1h6yPInnUQdiDDbogCUHl0lENHAULne1dQLy4fEJmFVIUAJUG6QGiW9tEB6JB+y80Hx1hyWks0migQBJFDECqCyKcQuLR3pGnrTHDPE0u4/dEV7OiqYVfrr6rKWG1RZKy1ic6DD4Yce+zofsavfgWf/KQkCIZvGXmeufmpri6mMxhLTwhNFEE6LZg2TVFba9p5nrlp6uiQ5HKiLz2iqkpQKBhXsu+bvqZNMzdXe3OKhGHRCjcCaMrsmUAsoM/ys9bf6GOFzwrfHrnooov4yEc+wpIlS8Z7KCNLlIWwBxG0Q6EdUdiKyG9HF9qRYQdEOSN2YQ9KFRBRiNA54x8UqlcIHTSy94InAceIoCqY52IwqOOCFoCHdqRZsFz0mmY6QgOvb6zmsh9dyAPPHg1M3iKRv/hFyCmnjE7fA9euy+c1/+t/wQsv7Nu5ymTMHF91dX8ATDptFgxWyqRE1NdDRYWx/mIxM/fa0mIst6oqI4DptBGwri4TwVkUwOEEUIehsdiz2aEF0Fp/o4vruqVyXq3wDeQrX/kK9957L1JK6urquOmmm2hoaNjnfi699FKOOeYY3v/+94/CKCcIWhmxivKIqBuCdsi3IvJvIwrN6LALGXYZ6y7Kg8qiogAR5c3KB6p3WQfdm+snHVCOsQpFBGEeYx2GvWaBAPze1XYkWnsIGaEjze+fPYj/c/W5vNV1OOO1AkI/Zh7L8zSxmLnYp9P9LsOZM2HGDJg1y6yUMWeOEZV9pShoxf9TrTVKqT3OKxddij/7GVxyiYdS+2b9FUut1dX1uz9931jVjgPTp0NDgzleU8rMuEabm43XoKbGVIhJJIyAFQtm19Ro6uqGV+A6iowA9vQACBKJnXMBwzC01t8oYYWvRIWvo6ODsrIyAK677jpeffXVYUV2KqV46qmnePvtt9m6dSt33303QRCQyWT4zne+Q2Nj42gPfWKgei03lUcEHcYqzG9D5N9GF9oQYTci6jGWX5RDR3lQBUSUx+TwGWsOJFo4CCEH/NKiXhdpaKzHSIEbBwRol8KW31L3sYcocPQIHEh/aI3vmwt1eblx/RYtnjlzoLGxX7ymTTvwosyDidnA56EYOEc2cM5s13mzgXR3wwknwCuv7NuNwmDWX1VVfwRrMll0k5ugFM8zc4M9PSawyHWNQE6fblIgOjpMQrtxqZq0ieGcx10FMB4384DmuqxQylp/I43neaVyIzHkj74kHLn7SlH0ALq7u4cdlSmE4Je//CW1tbVMnz6dhb1lOT796U8zfTRD9iYa0jMPUmi/CpIKrQpGDMNuRNgOhVZEdiui0IKOOpFBu3FxBgHoXqtQFRAqC1FoLDzdm7bg+KDjpoCnK0xtTq1A9+D7SdpuPZHkBTvoT2w34iWEJh7f+aJdX28sr7lzYd48I2D19SNTS3IgQ4nZcK0z6BcuKeVO+xzIRSiVMgsS/+d/ar7yFRiupWwCTsxc8P/f3nmHR1nme//zzExmMmmTAikkFCmuNJcjCOhSBNzD4isgxUVBwUXFsrsvyIqi2FgUX1xAEPcgykERPNguFXUVgwLLQSmigroWFgEhlQTSy9Tn/ePOPSUETJuZlPtzXc81Jc889z0p882vy0ShsjK8Lku7HY4cgaQkjYwMn0s0MlInI0Nkz2ZlwZkzGunpInnK49EoKhITIYqKRAKMnAZxPoxG8bOMjRVlELIgvuariF8cD7ruxGRyYzabMJkMNdmh4vX+91tBArYiBLRLiw9g0aJFvPzyy9hsNnbu3NmoYvatW7eyf/9+HnjggSDssJXjcdVYhdVozjJwFKPZC9Ec+eiOEjRXCZqrCnCCyy56hOpONHcVml4Tr/ImxWiiZZhuhJLD4MzDNeQfkHxZ8N9GE1yNQfVdIgAAIABJREFU8j4Epuj7Pw4lp0/DyJFw8mTDPv39Mz+lK7djRyEm1dXCcktPF/9QWCwirmex6GiacH9WVwv3aUaGsBCdTo3iYvF1m024QOPj69fSzOMRWboeT+DhcnlwuTyIecUmNK1uNdW0QEG80G17pY20K4P26OqsT79OgCeffJLq6moWL66rG8iF2bNnD5s3b+Zvf/tbk/baLtA9NS5SO7iq0FzF4CxBqzqN5ihAd5VhcJbWfL3GKvQ40Vw1GaQet4gVVmWD4zSufk9DxrhGbaUuMavPCJzarsX6uBpbIosWwapV0JA4aUSEEMCOHX0iKO/L+kebTbg/ExJ0LBYNs1kIoMMBZ8+KtTp0EAXyUVGiBZoUwLg4vNmkTXEly+QXTTNgMJgAg7cmU4qkf52mfK4upAD6i2Fd99saSvhasfDVl5MnT3LNNdfw7bffNvi133//PY8++ij//d//HYSdtQM8LuH+dNdYhc5SqC7E4MhDd5agOUvR3DWJMy4HOg50x1kM1Tm4LnkMUkb4LtWEuJm89Rew5nI1tlSOHxfW35kzjbP+4uOFiImaPeE6rqwUFlVysrAArVbR/SUiQmSBFheL5gEWi4j/paSIHqDV1UIAdV3zxgATExvvjvYvfZCJGhf6Gep6oCjWFkb/52rjb0HWPvyfb01Y6pN91DpQMT5//v3vf9OrVy9AuCsvueSSRl0nKSmJoqKi5txa+8JgAkxgtKKbE8QnUJwTt8cBrip0x1lv4gz2AjRHKVpEB9zmVBxEoZ2nrcr54mbya/6P2ysXXQQnT8KcOTqvvFJ/8Ssv9zUEcDh890UNoBCI/HzRNScjQ6NjR7BYRJee6Ggdm02joAB+/tkX/0tM1ElLEy7RoiKdsjKNwkJhOfoPxK0vBoMBg8Hgtf48Hs8FEzY0zSdQF7I2pUDWFkd5SBdsXf9ryesnJLRsIWwjlt4v0i4tvilTpvDjjz9iMBjo2rUrzz33HOnp6Q2+jsvlYsiQIezatav5N9mGaZCrUXfXxAqdGNzlaK4yNHcFenQPtMikVulqbGl88QVcc41oPdYQYmN91l9SUuC0+cpKIQDx8aKkIzbW5/6MitKprhYJLjJDNCVFukhFF5eiIpEMEx3tE8D6TnXwp6HWX3NQWxD9hTIhoWW7R9tQuzJQrs7g0VoaVQeb5nI1/mLcrKawXY4PUjQPbjc1Q3Ub9j01m6mJz52b/OJ2C2vQbBbClpEhRhOZzSL702rVqKzUKS4WE9ytVvF66QKVSTAul0ZUlBim27Fj/Qrha+OL/WltKV2/2VHCJ1DC9wu0ZeHz7wbib5Wdr/GwpKVmNSp+mXffhVmzROJJfdE0n/VnswnRs9lEHC8mRiS/yBq+9HQRGzSZhAszKkonMlKjrEwIoN0u3I0dOohyB6sVXC4hgA6H6A8aH+8TwIb87xMO66+10YbalYESvuAxePBgPvzww1Y1v6qxKfrytrVnNSoujMMBV18NX3zROOtPJr3YbMKCS0sTAlVR4evs0rmzKHiX7k/RQEDMQiwuFq7SiAghpqmpomjd5dIoLRVuUotFCGBycv16gfqjrL/z016Er828w8ayYsUK7r33XgoKCujQoUODX5+YmEhRUREpKSlB2F39aWo3EKPRWO9uIIq2jdkMu3fD88/rzJ8Pul4/VRFlC6K0oapKHHa7ELxOnUS8r7IS8vJEMXx6ukZaGoCw5qqqRCaoSHQRRfAFBSIJJj4e75gkt1skwOTnizihzSbKI4SA1p1d6Y/8nfZ4PNjtdtX2zI/2ktzSroXv1KlTZGZm0qVLlwa9Ttd1ysrKyM/Px+1288Ybb2CxWLj99tubdX8XcjU2phuI/Jr/Y4XifMyZA9ddB6NH6xw/Xr8PRI9HZHTKji92u8/VmZQkk1jEOT/9JKy75GSNxEQx9b2sTEy6t1hEt5eEBCGAcvyUzaaTmqoRF6fXdHPROHNGDBGWfxLnFqOLmGFEBN5bo9GA0WhA02TmpwOz2az+LtoJ7Vr47rnnHp566qmAgvZfIisriwkTJhAXF0dKSgoFBQUcOXKEwYMHo+t6vf5jamo3EOmKUGKmCDbJyfDtt/DQQzpPPw31LXr3t/5kyzN5X05+dziEoJWXCyswIUGrqQkUCS12u1YzMFcnKUl0gSkpEdMg4uI0byZoXJz4G/BlT+o13VxkecG5e/aJohHQMBo9GI0OIiMNREWZMJsN51iO7YH2YvG12xjf1q1b2bFjB6tXr6Zbt24cPHiwUa7OxYsX06tXL/5PzbyZX3I11hbHxjQeVijCwU8/iYbXDS16t1pFkktysrD24uLkCCMRB5TWoa5Tk7zi6wmqaTpGoxBAi0UnIkIIX0mJ7/y0NJEIExPjs/r8a+48Hq1W3Z0eUHIghVHE/sQ/pRaL6PkpBdJkEkdkpLAaTSafIJpM4py2oBltLObZPmN8F2pbtnTpUjIzM5u8RnZ2NgcPHmTs2LHn7QIib9t6NxBF26ZHD1F4/oc/6LzxRv0/5auqhPUli93l8ODqapH5KUcf2e0i9peTI/qKJiRASoqo5XM6RRzQZBKF8PHxvkzQo0chN1dYizabdGXK0glxWxe67rMKhQgacLnA6fTg8Thwu4243aIRtq6fK2z+7lSTyedKPV+ssTUIo7L4BG3S4vvmm28YM2YMUTUFQVlZWXTq1IkDBw40eMpCVVUVc+fOxW63s3r16laV3alQNJYdO+CGG6CiomEflNHRwpKTY46SkoQVJadpREcLgZTxQZNJWIgpKeI2IkJYgCaTEDSLRaO8XAigrotraZpPiKTgmEzi3MhI8byYIq97rTf/z3tN81l/LhcYDBHouqHOHp8uV01paa1PSl0/t3WZvyjKKfby+ZaiN22oTyeocoYL0xRXJwj35erVq3n33Xd5+eWXSUxMbOYdKhQtD6dTdHz57LOGlz2IjizC4pNiaDb7eoGKuJ0QwMpKIRAxMb5SCbNZCKDRKF2gouBd04ToOJ3CpSndmP79OP1dl/4JMLWFUdM8RER4MJk8mEyGczI/db3u7ixSDAPdqeI1cn+67ttHjx4Nb8sWLNqL8LVpV2eo0DSNefPm0aNHDyZMmMBLL71Ez549w70thSKoRETA9u2webPO3XeD213/xBeHQwhEdbUobI+JEbeVlSLTU3ZxiY+nZpKDcIOWlvoSYVJSRC2gy6V5+2zabGIwLvgSXsR6YhyS7KXprBkN6XDIXWneJtS6Li1GkfkJHgwGDxaLi6goE1arwSuc0oKLjAy0+oTV+MvC6PEIcW8JwucfomnrKIuvmTl8+DCzZs1i2bJlDB8+PNzbUShCwtmzMGYMHDnSsA9OOb8vMlKIX1SUEMDoaN/zshBeCmBlpRAPk0lYgCkpQiil2zAmxmfNmUy6N/YmP9NlpqemCTESAigEVIqV0+mL/0lcLuH+1DQDZrM4pJtUruGf/OIvjEZj3Vaf2y2+lpTUTD+IJqBpWlsL1ShXZyjJzc1l6tSpzJw5k5tvvjnc21EoQsZf/wrLlkFDZv2BEIOoKCEg0dFC/Gw2nyBaLIEjkVwuIYAOhxAYm00IYEyMmAZvtWpeqwvwJqdIkZJuRqNR97o2ZWamzPSUAiXqEIUwulwenE43LpeGrpvQNF/ii7Tg5LQHeU2DwSeMFos45NdFtqrv/YWTNtanE5TwhZ7KykpmzpzJRRddxKOPPqqyOBXthuPH4aqroLCwcW4zi8VnPUnrLzZWHDI+GB8vRFDThDBVVorXxseLxJnOnYUVKLtvGY26V8ikxSfdnvKoSxhNJt1ruck/YTnx3eNxA8aa7E+D10J0uQLHFPmv6x9jlOKnaeI9XXpp42cQNgdK+Hwo4WsE+fn5fPfdd+Tk5LBhwwZOnTrFf/zHf9CzZ08WLVoU7u0pFEFH1+GWW+DNN5sWM4qOpmaUkU/wYmKEKFqtvskQYpyRbxiuzYZ3mntEBN6kFf+yA+mOFBaarLv1WXz+2ZpSwDTNJ4IGgwdNc2M2g9VqwmQy+gmreJ10m8p4ory+KJsIjAv26ycEO1y0sT6doIQvtHz00UdkZmaSmppKamoqhw8fZvv27WzYsIHevXuHe3sKRcj4+GOYPr3hZQ+1kW5Cq1UIYEyMEDerVRyxsSLeJ5pZi6QZ6TqUlposK5BlDvK+f4mBFEQpmNIA0jSfxegvjELkdFwuDwaDAbNZw2IxBKzlX7ogY4gSKYBOp3gPv/pV+Ob1KeHzoYSvmdi1axdz585l3bp1XHrppeHejkIRMhpb9nA+pLUnBTAuzmcF+rtBExKE4EiBkhaW/33wJZ74d2LxJcf4YnD+YugvZsIS9I080nVR9qDrgaUPcO61RTmGr6yiUyfx3sKBHNXUhlDC1xL497//zbRp01i0aBHjxo0L93YUipCyfj3cc49oIdYcSCtNZoLKQ4piYqKY/h4VFShS/kksTmegEEo3pKy988/GlBacbFHm6xDjL4weNM2D2axhtRqJiJCdm8Sa/qUM/vFFSUwMDBwYHqtPCZ8PJXzNzNmzZ7n++uv53e9+x913391u6mYUChCtyMaMgWPHmvf33t8KjIvzWYNJSUIM/TMrpVBJa8s3sUFcS8byZIKKbG0ma/FcLnHIDjFu97luVE3z1HSLMRAZqdWUP/hKHOReavf41HWR5BId3azfnnrRxvp0ghK+loXD4eDOO+/EaDSyfPnytpZJpVD8Ihs2wKpV8NNPzSuAsjwgMlIIYHy8mPouhU6KmiwzkBmWMmnFYvG5N/1bjMlz/A+ZsCKzNf2tRbdblji4MRgMNY22DQHxRf/Yon98MSlJWH2hDrcp4fOhhC9I6LrOU089xSeffMJLL71EfHx8uLekUIScqipYuhQ2b4bTp5tXBC0W4eaULdBqz+STpQPSTSmR7k3p0pRWmUykkff9ryUtPlkWYTCIBBuXS685PICxZlKEwetGlfV//vHEiAgYPRp69WrWb8cv0sbalYESvpbLW2+9xdKlS9m4cSOdO3emoqICm80W7m0pFCEnJwcWLYIPPhADZpsLs1m4O2UDaykyMl4na/fkc1LU5LmRkULIZH9N/1ih/3QGfytRWp6+vp864AZExxddN2C3n9vOTMYae/aEqVNDG+tTwudDCV+Q+Oijj3j11VfJy8vj559/5vjx43Tt2pXx48ezePHicG9PoQgrX34pRHDvXtF8ujnwb07tX0Ree2K7PCewkD3QDepffG6xBLpA/V2q/hmcckSS0eghMtKA1SpKH/ynQ/gL69ixohg/VFhaQsPQ5kUJX1MoLi7mtttu49tvv0XTNDZs2MAVV1zRpGv+/PPPFBcXk5qaSocOHbxtzu644w6mTZvWTDtXKFo3ug7vvAP/7/+JSfANbYVWFwZDYA9OybkTG3wiKe+Dz8Xpf5608GScTmqItP5kDaB0h8qJECaThslk8Haq8bcce/aEa68NjdXXBvt0ghK+pjFr1iyGDx/ObbfdhsPhoLKyMigxufLycqZPn07//v158MEH25rbQaFoEk4nPPssrF0L2dnNI4BwrghKkar9XF3C6F/755v9d64b1b+DjM/S1L3JLgaDhsFgCIgVRkXBrbdC//5Nfqv1+F60uXZloISv8ZSUlDBgwACOHTsWEiFyu90sWLCA7Oxs1q5dS2RkZNDXVChaG6WlsGQJvPIKlJQ0/9+ldFXWrrOTz9UWR/8p7P4i6e9C9T/H/zwpksLSMwQUyA8cCH/+c/AzPJXwBdLuhe/QoUPMmTOHPn36cPjwYQYOHMjq1auJDnKhzbp169i8eTObNm0iOZSOfoWilXHqFCxYIGYDVlcH/59TmeUpC9ElUizrcqP6lzH4xxLlff9kGuFGFdaf1SpinWPHBvc9tcF2ZaCEr/EcPHiQoUOH8umnnzJkyBDmzp1LXFwcS5YsCframZmZ3Hfffaxfv54+ffoEfT2ForWzdy889BDs3493+nqokY6hukTwQm5U/7IIYTEK8evdG958U7g+g0V7E742Va0YDDIyMsjIyGDIkCEATJ06lS+//DIka//nf/4nW7Zs4fbbb2f79u0hWVOhaM1ccQV88omY1v788zo9euiE+v936R6ty/KDwLZp8nynU9Q0lpdDSQmcOQP5+R7y8jzs2QNPPx3cPbe3fAIlfL9AamoqnTt35scffwTgk08+Can11bt3bzIzM1mxYgUrVqzg0KFD7Nq1K2TrKxStEU2DGTPg66+hqAgeekgnOTn8Dix/Uaxt+fkXv8vEG10Hh8PDq68GTnVQNA3l6qwHhw4d8mZ0du/enRdffJGEhISgr7tz507uu+8+3G7R9ig3NxebzcakSZPUXD+FohEUFsLixcIVmpcnLEOHo+VbOwYD/OlP8NRTwbFV2mC7MlAxvtDgdrsZNGgQ6enpvP/++02+ntPpRNM0r+9d13WWLFnC/v372bBhA7GxsU1eQ6Fo77hcomvMgQOwb5+wEk+eFJZiZaV2XpdlqImJcXPypIGoqOafoKCELxAlfA1g5cqVHDx4kNLS0mYRvvPx6quvsnLlSjZt2kTncI5sVijaAVVV8M03QhS//BJ+/BHy86G4GOz20FqL8+fbeewxkYjSnELVBtuVgRK+4JOVlcWsWbNYtGgRK1euDKrwAezdu5c777yTNWvWMGjQoKCupVAo6kbXhQh+/jl8+qkQyFOnxPilykpwu5tXTKxWN0ePuomOFlZac83PU8IXiBK+ejJ16lQeeOABysrKWL58edCFD+DEiRNcf/31zJs3j0mTJgV9PYVC0TCqq+HIEWEtfv65uJ+VJTI3q6oaJzRz5uisWOHB7XajaVqzuCmV8AWihK8evP/++3zwwQf813/9F7t27QqZ8AGUlpZyww03MHToUP7yl7+0xV9ehaJNouvCXfr556L+8Kuv4OefhbVYXg4u1/n+lnXKy0HXPXg84pDT0xsjgG20Tyco4QsuDzzwAJs2bcJkMlFdXU1paSmTJ09m8+bNIVnf5XIxb948SkpKWLNmTVv9JVYo2hVOJ/z0kxDFfft81qKuw9GjvvM8nqZZf0r4zkUJXwMJtcXnz6pVq3j99dd5+OGHqaqqol+/fmRkZIR8HwqFIrRIy68x1l8b7dMJFxC+Ntejpr2h6zpXXnkldrvd+4t+0003MWnSJLp16xbezSkUipAgJjsYvNafx+NpqyUKzYKy+ELEqVOnmDlzJvn5+Wiaxpw5c5g7d26zXNvlcgX02fvmm2+4+eabefLJJxk5cmSzrKFQKFoHDbX+2mifTlCuzvCTm5tLbm4ul112GWVlZQwcOJB33nknaO3P8vLymDp1KjNmzGDWrFlBWUOhULRc6hv7a4/Cp+zgEJGWlsZll10GQGxsLL179yY7Ozto66WmprJ9+3Z27tzJww8/jKeltJ9QKBQhwWAweOv87HY7Doejzs+B9pgJroQvDJw4cYKvvvrKO/EhWFitVl599VWsViszZsygoqIiqOspFIqWhcFgwGQyYTKZcLvd5xW/9oYSvhBTXl7OlClTWLVqFXFxcUFfz2Aw8PjjjzN58mQmTJhAbm5u0NdUKBQtCymAmqadY/21R4tPxfhCiNPp5Nprr2Xs2LHMnz8/5Ovv3r2bP//5z6xdu5YBAwaEfH2FQhF+ZOwPRNuzyMjItpr9qZJbwo2u68yaNYvExERWrVoVtn0cPXqUadOmcd999zF48GAKCwvp27dv2PajUCiCj67rlJWVkZOTQ25uLjk5OeTk5JCXl8e4ceOYMGFCuLcYDJTwhZs9e/YwfPhw+vfv7/3vaunSpVxzzTUhWf/jjz9mzZo15ObmYrfbOX78OKmpqQwbNoxnn302JHtQKBTNi67rbNu2jS+//JIRI0Zw+vRpr6DJ2+LiYgBiYmLo1KmT90hPT6dTp0707duXlJSUML+ToKCEr7Wwbds25s6di9vt5rbbbmPhwoXNct0zZ85QUVFBamoqZrMZp9PJ3XffjcfjYeXKlW21c4NC0SrRdR23201BQQHZ2dnecigpZnl5eRQUFKDrOhERERQVFVFVVcX1119P//79vaKWkZFBfHw8mqa1x1ieEr7WgNvt5uKLL2b79u1kZGRw+eWXs2XLlqDV+um6zooVK9i2bRsbN24MyVR5haI9o+s6uq5TVFTkdTvWPvLz83E4HBiNRpKTk0lLS/MKmb+gJScnYzAYvIK2b98+tm/fzsMPPxzmd9liUMIXTHRdR9M0nE4nTqeTqKioRl1n7969PPbYY3z00UcAPPnkk4Bogh1M3n77bR5//HE2btxI9+7dg7qWQtFW0XWdiooKsrOzva5GKWbycWVlJZqmkZCQEOB2lEdGRgZpaWlYLJb2aKE1N6pXZ7CQoldeXs4HH3zAjh07uPfee+nZs2eDr5WdnR0wUT0jI4P9+/c353brZNKkSXTt2pUZM2awfPlyfvOb3wR9TYWitaDrOkuWLOHqq69G0zTy8vK84iaFraioCE3TiIqKChCyLl26cMUVV3gttdjYWCVoLQAlfE1Aip6u6zzxxBPous5VV13VKNELN5dddhkffPABU6dO5dZbb2X69Onh3pJCEVR0Xcfj8VBQUBCQ7SgttNzcXAoKCvB4PFRXV7N27Vouu+wyRo4cSUZGBv369SM9PZ309HQSExPbaxytVaKErwnIX/Ibb7yREydOMHz4cE6dOtXo66Wnpwe8Pisri/T09CbvsyHrf/zxx8yYMYOjR4/y0EMPtdX6HkUbRsbRiouLA5JC/F2OeXl5OJ1ONE2jY8eOAVba0KFDvfG0lJQUjEYjmqZRVlbGggULmDFjBr169Qr321Q0ARXjawL/+te/eOGFFzhx4gSrVq3CZrMxZswYpk6dyoMPPtjg67lcLi6++GI++eQT0tPTufzyy/mf//mfkNfZeTwe7r//fk6cOMFzzz2H1WoN6foKxfnQdZ3KysoAC01aZ/K+bM1ns9lIT08nLS0tIDFE3kZGRioLrW2jYnzNzfPPP8+PP/5IXFwcb7zxBhEREVRUVDBr1ixvY9iGYjKZePbZZxk7dixut5vZs2eHXPS++OILDh8+jM1mo7CwkIsvvpguXbrQu3dv1q9fH9K9KNoPr7zyCkOHDsVsNgek7/tbaGfPnkXXdW8czV/QBg8e7L0fFxenBE1xQZTF10i+//57jh07xrBhw7DZbBw8eJB//vOf/PDDD8yZM4fLL78cj8cTdFfhggULeO+99zCbzfTo0YMXX3yR+Pj4Rl/vrbfeIicnx/uhcuzYMZYtW8b69evp169fM+5c0R6QcbTCwsLzpu8XFBRQUlJCTk4OvXv3ZuDAgd4Ufv/0/aSkJBVHUzQEVc4QDGRyy+7du1m7di2jR4/2Br2Li4vp379/0PeQmZnJ6NGjMZlM3H///QAsW7asWdf44YcfuPHGG3nkkUcYO3Zss15b0TqRcbTS0tI63Y7ycDgcaJpGhw4dAiw0f0FLSUnBZDJRXFzMHXfcwcKFC70jvBSKJqCELxhI4bvxxhu55pprSE1N5ccff8ThcLBv376Q/wG//fbbvPnmm7zyyivNfu3CwkKuv/56xo8fz5133tns11e0HHRdp6qq6rwWWl5eHqWlpWiaRlxc3DkxNClonTp1wmq1KgtNES6U8IWCZ555hv79+zNq1CjeffddSkpKuOmmm0L2hz9+/HimTZvGTTfdFJTr2+12br/9dqKjo1m2bFlbndrc5vB4PHz44YeMGzcOt9tNfn5+nVZaXl4eZ86cQdd1IiMjSUtLO6driDzi4uJUxq+ipaOSW4KFtPoAysrKGDVqFMeOHeOVV15h8eLFzSJ6V199NXl5eec8/8QTTzBx4kTvfZPJxIwZM5q83vmwWCxs3LiRpUuXMm3aNF588cWQzBRUXBjpdiwsLDynp2Nubi7Z2dl8+eWXOBwOunXrdk63kBEjRngFrUOHDgFtsBStl27duhEbG4vRaMRkMnHw4MFwb6nFoCy+ZsLpdPKXv/yF7t2789VXXzFz5kzGjBkTIIzB4qWXXmLdunV88sknjW6X1lBee+01li9fzqZNm+jSpUtI1myP+MfR/DuG+LfEstvtaJpGYmLiOd33pbWWmprKW2+9xfr16/n444+VsLUDunXrxsGDB+nQoUO4txIulKszVOzatYuYmBgGDRoUkvW2bdvG/Pnz+ec//0nHjh1DsqZk//79zJkzh9WrVzN48OCQrt3a0XWd6urqgNhZ7XEyJSUlaJpW5zgZ/3hadHR0vYXMbrdjsViC/O4ULQElfEr4gk4oShfqomfPntjtdpKSkgAYOnQozz33XMjWP3HiBJMnT2bq1Kn069cPh8MRshmDLYVjx45x0UUXedvXuVwubxus2gkieXl5FBYW4vF4AuJotQUtPT29PY+TUTQDF110EQkJCWiaxh133MGcOXPCvaVQo4RP0bw8+uijvPfeewDExsZy9OhRunXrxs0338zMmTPDvLvmR8bRzp49e04LrK1bt1JYWEhKSgputxuj0UhKSoq3yLq2oNUeJ6No3bjdbgYNGkR6ejrvv/9+uLfjJTs7m/T0dE6fPs1vf/tb1qxZw4gRI8K9rVCihE8hWLFiBffeey8FBQVNcoG4XK6ArE6Xy8X8+fMpLCzk73//e6typ+m6Tnl5ecA4Gf/b3Nxc7zgZGUfzz3bs1KkTe/fu5Y033iAzM7NJDQQUrY+VK1dy8OBBSktLW5Tw+fPYY48RExPDvffeG+6thBKV1amAU6dOkZmZ2SzJKLVLGUwmE8888wzPPvss1113HZs2bQp7bEHXdex2+zntr/wfFxUVAXjjaFLQunbtypVXXukVt5iYmAtaaMOGDWPKlCnYbLZQvT1FCyArK4t//OMfLFq0iJUrV4Z7O14qKirweDzExsZSUVFBZmYmjzzySLi31WJQwteOuOeee3jqqae8JRDB4E9/+hM9evRg4sSJbNiwgV/DzbjRAAAKWklEQVT96ldNup7T6SQiIiLgOV3XcbvdAeNk/JND8vLyOH36NB6PB4vFQmpqakBiSP/+/b3uRxkDaQ63oxri2/6YN28eTz31FGVlZeHeSgD5+flMmjQJEN6Y6dOn87vf/S7Mu2o5KOFrJ2zdupX09HR+/etfB32tcePG0blzZ2666SYef/xxRo8eXa/XyThaUVERubm5ZGVlcf/993PllVdisVi8VprT6cRgMNCxY8cAl6Mc+CnjaHKcjKJ1Ul1dzYgRI7Db7bhcLqZOncrixYvDvS0v77//PsnJyQwcOJBdu3aFezsBdO/encOHD4d7Gy0WFeNrQ1yo0H3p0qVkZmZis9lCluacn5/P1KlTmTZtGn/4wx+oqKg4px7NP+OxsrISgPj4eK+FFhMTw6uvvsr48eO56667SEtLU+Nk2gm6rlNRUUFMTAxOp5Nhw4axevVqhg4dGu6tAfDAAw+wadMmTCYT1dXVlJaWMnnyZDZv3hzurSkEKrmlPfPNN98wZswYb3F7VlYWnTp14sCBA6SmpgZ17aqqKkaPHk1+fj6pqane1P3aPR3T09OJjY2tU9Cqqqp49913mTZtWlD3qmi5VFZWMmzYMNauXcuQIUPCvZ1z2LVrF8uXL2+xyS3tFJXc0p7p378/p0+f9j4OZWGr1Wrls88+Q9f1Rtc5Wq1WJXrtFLfbzcCBAzl69Ch//OMfW6ToKVofqsusIuhomqYaGrdATp06xahRo+jTpw99+/Zl9erV4d7SORiNRg4dOkRWVhYHDhzg22+/DfeW6uSqq65S1l4rQn0atUNOnDhxXmtvzZo1XHLJJfTt25f77rsvxDtThBKTycSKFSv47rvv2LdvH3//+9/57rvvwr2tOomPj2fUqFFs27Yt3FtRtAGUq1PhZefOnWzdupXDhw9jsVgC3KOKtodslwai+07v3r3Jzs6mT58+Yd6ZoKCggIiICOLj46mqqmL79u3eYcsKRVNQwqfwsnbtWhYuXOjtupKcnBzmHSlCxYkTJ/jqq69aVAwtNzeXWbNm4Xa78Xg8/P73v+faa68N97YUbQCV1anwMmDAACZOnMi2bduIjIxk+fLlXH755eHeliLIlJeXM3LkSBYtWsTkyZPDvZ1687//+7+sX7+eKVOmMGHChHBvR9HyUFmdCsGFav1cLhdnz55l3759fP755/z+97/n2LFjqmauEcyePdtb4NxSEzJAdMaZMmUKM2bMaDGil5+fj9vtplOnToD43TSbzSxYsCDgvKioKL744gvcbjcTJkwIyexLRdtAJbe0Mz7++GO+/fbbc46JEyeSkZHB5MmT0TSNwYMHYzAYKCwsDPeWWyW33HJLi0/E0HWdW2+9ld69ezN//vygr+XxeM55ri6P0549e3jnnXe8j91uN8ePHwfExIGzZ88CMHDgQFatWkVpaWkQd65oiyiLT+HluuuuY+fOnYwaNYojR47gcDjC3mi6tTJixAhOnDgR7m1ckE8//ZRNmzbRv39/BgwYAMDSpUvrNU+xqqqK6upqEhIS+Omnn9iyZQsVFRUcOXKE5ORk7rrrLi699FLv+f79UKVl5m+dFRUVYTKZiI6O5sMPP2TXrl3k5uYydOhQBg0axP3338/s2bPZvXs3w4cPZ+3atURGRmIymbxJWMraU9QXZfEpvMyePZtjx47Rr18/brjhBjZu3Kg+TNoww4YNQ9d1vv76aw4dOsShQ4cCRE9aabWtshdffJHo6GiefvppAA4cOMAjjzzCgAEDmD59Opdccgnz5s3j7bffBuDs2bPs3LmTN954g6+++sr7O7Vnzx5+85vfMH36dIYMGcLChQs5fvw4DocDj8fDoEGD6NOnDwaDgZMnT7JmzRq+/vpr7Ha799pdunShpKQkFN8uRRtCWXwKL2azuVX0Gdy2bRtz587F7XZz2223sXDhwnBvqU1Sl5UGYLPZGDduHH/9618B6NGjB3379g3orhMfH8+jjz7KpEmTeOaZZzh27BiJiYns2bMHm81G9+7dcTqd7N27l02bNtGtWzfuuusuXnvtNZ588kmmTJninSJSVFREWloa0dHRVFVV8etf/5qff/4ZgNTUVOx2O+Xl5cTExITy26NoxSiLT9GqcLvd/PGPf+TDDz/ku+++Y8uWLS226Lo1U1xczHvvvce6detYt24dmqZ5Lb+0tDTOnDnjPTcjI4OcnBxAJMsATJgwgezsbHbs2MHu3bt54oknmDhxIgcOHGDTpk0A3l6tcpzTLbfcwmeffYbdbqeqqgq73Y7b7aZjx46YzWbcbjdWq5XIyEiqq6txu91ERUVhMBi8cT+Foj4oi0/Rqjhw4AA9e/b0fljecMMNbN26tcUUXbcFXC4Xq1at4uTJk0RHR5Oeng74YmgdO3akqqrKe35aWppX8OTsRDnncPfu3eTl5XHrrbeSlJTE2LFjvXPhEhMTMZvNlJWVERsbS2VlJTExMVitVhwOh7eeNC4ujoiICAoKCkhNTcVsNnP27FlKS0tJSEjAarWSn5/fLAOWFe0DJXyKVkV2djadO3f2Ps7IyGD//v1h3FHd3HjjjezatYvCwkIyMjJYvHgxt956a7i3VS9cLhfr1q1j//79dYpJfHw8uq57BUvTNEwmEzk5OXTq1Am3243RaMRqtRIVFcW4ceNYsWJFwDV0Xcdms1FYWMjbb7/NzJkzee211xg6dChpaWl06dKFadOmcckll3DnnXeiaRrZ2dmkpqbSuXNnNE3D5XIB0LVrV6/FqVDUByV8CkUQ2LJlS7i30Ch0XScyMpLhw4fz4IMP0rlzZ377298ycuRIjEYjANHR0VgsFvLz84mNjQWEhSfLFYxGIwsWLGDkyJHccMMNzJ49m5UrV9K9e3cOHTrEpZdeyrXXXktERARDhw7ltdde44UXXiAuLo6HHnoIgCVLlnD48GF69epFUlISO3bsIC4uDiCge8uOHTvIzMxk/Pjxofw2KVo5SvgUrYr09HROnTrlfZyVleV1xSmajnRnvv7669jtdu666y5efvll+vTp453dGBkZSVxcHDk5OfTs2RMAi8XC7Nmz6d27N99//z2JiYksWbKELl268MILL7Bq1Sr2799PWloa6enpREREoGkaCQkJjB8/nunTp3v34PF4GDx4MIMHD/Y+ZzabA/bpcrkwmUw4nU7+9re/1asEQ6GQ/FLLMoWiRaFpmgk4AowBsoHPgem6rv8rrBtrQ2ia1hNIBuzABOAksEnXdYffOa8Db+q6/nrN45uAXsAPQB7wna7r+fVYa2PNucs0TYvQdd3p9zUDoOvqQ0rRzCiLT9Gq0HXdpWnan4CPACOwQYles3Mp8EfAAXwDbNd13aFpmuYnQqeBAcDrALquX7AORhOmpMwi13Vdl21c/i9QWfOk0/81fudcEE3TjIBHCaSiviiLT6FQ/CK1RI+afz6eBB7Rdf3pGkscwIOy0hQtHCV8CoXiHGrcjLJtzwWtqdqiqFC0dJTwKRSKRlHjvkSJnqK1oYRPoVAoFO0K1bJMoVAoFO2K/w8uCSrX+wxL5QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(tot_s_span, trajectory, yn, len(X))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "py37",
   "language": "python",
   "name": "py37"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
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    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
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   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
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    "_Feature"
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   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
